Where power lies in Britain. The Mother of Parliaments, which wrested power from kings, is losing leverage to 10 Downing St., to bureaucrats and TV

A good place to begin looking at British democracy is in the splendid Victorian ornateness of the residence of the speaker of the House of Commons - the man whose wig and gown symbolize the ''Mother of Parliaments.''

Coats of arms emblazoned with lions, birds, dragons, and harps . . . gleaming brass lions and unicorns flanking vast marble fireplaces . . . paneled walls and high ceilings . . . chandeliers . . . azure and gold paint. . . gilt-framed oil portraits of bewigged former speakers. . . . All these fill the speaker's newly restored state apartment, at the Commons end of the Palace of Westminster.

Sitting amid this splendor and talking to Welshman George Thomas, the speaker who has just retired, is to be reminded of the example Parliament set when it wrested independence from the monarch centuries ago.

Yet many analysts today express concern that Parliament - the House of Commons and the nonelected House of Lords - is losing ground to other power centers in Britain. In particular, they say that Parliament must keep more effective watch over the executive and must represent a wider variety of voters if British democracy is to keep pace with change, and if the country itself is to emerge more fully and effectively from its period of empire.

These analysts suspect that Parliament has gradually become a prisoner of its famous traditions, a ''talking shop'' swamped by changes that it has less and less power to balance and check. What can be done, they ask, to give the voter, through his Parliament, more than a once-every-five-years influence on decisions?

Pressures on today's Parliament include:

* The growing power of the prime minister and her or his personal staff of advisers.

* The experience, resources, and tradition of secrecy within the nonelected civil service, which considers that it serves Cabinet ministers rather than Parliament.

* The modern strength of party discipline in forcing backbenchers to vote the party line rather than their consciences.

* The role of television in spreading information and creating public images.

* The meager staff and monetary resources available to the average backbench MP. Salaries are still low, and members are torn between amateur and professional status.

Moreover, the Commons that was dissolved to make way for the June 9 elections contained no blacks, no Asians, and only a handful of women. The House is still narrowly based, containing a sizable number of Tory farmers, Tory and Labour barristers (trial lawyers), and Labour Party trade unionists and teachers.

Of course Parliament, and the House of Commons in particular, retains a degree of ultimate authority. Prime ministers must keep their majorities there intact on important votes, or resign - as James Callaghan had to do in early 1979. And the role of a ''talking shop'' is still important at a time of crisis or war.

Yet the former deputy editor of the Times of London, Louis Heren, worries about ''the all-powerful transient majority.'' He is referring to the way in which the government of the day can use its majority in the Commons to steamroller legislation through despite objections.

Others call it the ''tyranny of the majority.'' They argue that more restraints are urgently needed - perhaps in the form of more powerful backbench committees, a switch to proportional representation in elections, and increased decentralization.

Prominent Tory backbencher Hugh Dykes, MP for Harrow East, says the Commons is being overshadowed and weakened by old-fashioned attitudes and inflexibility in the face of change.

''A lot of modern MPs,'' he said in an interview, ''are exhausted, underpaid, understaffed, and overworked. Parliament simply cannot cope with the executive branch any more. Paradoxically, the House of Commons, which likes to think of itself as the strongest chamber of its kind in the world, is in danger of becoming one of the weakest.''

John Griffith, professor of public law at the London School of Economics, argues that Parliament urgently needs a new focus of committee power to supervise the executive branch, especially on financial affairs.

In a recent book, Louis Heren writes: ''Parliament has become a jousting ground where forces not necessarily representative of the national majority can impose their ideological will or whim. . . . Legislation can be bulldozed through without proper debate. . . . Control of the national pursestrings has been largely lost because immense sums of money are voted through on the nod. . . . Policy can and does swing violently from the ideological left and the ideological right.''

Adds author Anthony Sampson in his book ''The Changing Anatomy of Britain'': ''. . .Most observers would probably agree that the House of Commons over the last two decades has lost more influence than over previous periods. . . .''

Besides the power of the civil service and the competition of television, he pinpoints the clubby parliamentary rituals - which look to him increasingly anachronistic - and the European Community taking more economic power in subtle, backstage ways.

''It is now only in rare national crises that Parliament again becomes the dramatic heart of the nation which can influence events . . . as it was during the Suez and Falkland wars,'' Mr. Sampson writes.

Defending Parliament is the courtly man who has just retired as speaker, George Thomas, a former secretary of state for Wales and still a Methodist lay preacher, who will now become a peer. To him, Parliament - and democracy itself - is in excellent condition.

In an interview, the ex-speaker referred to ''an instinct for fair play'' in the House. Debates were noisy but impassioned. Televised coverage, he thought, would eventually come, just as radio coverage is already here (making his own voice, calling ''Order! Order!'' known up and down the country). Television, he said, would involve the voter more.

''Ithink,'' he went on, ''that if this place went dead, democracy would die also. . . . But it is safer here than anywhere else.

''One major effort to strengthen the House came in 1979 - setting up more ''select committees'' to question executive ministries and departments. Speaker Thomas conceded that if these backbench committees grow more powerful, they might keep many members from the floor of the House itself and weaken its influence as a debating chamber. Every effort should be made, he said, to bring committee reports to the floor of the House for debate.

Mr. Thomas is sensitive to the distaste with which many British people have listened to the interjections, boos, and heckling of broadcast debates. But, like many older public figures here, he clearly felt uncomfortable at the idea of changing the electoral system (first-past-the-post) to proportional representation. Nor did he accept the thesis that prime ministers, Cabinets, and the civil service could remove or disregard the ultimate powers of Parliament.

One of his deputies, Ernest Armstrong, Labour MP for Durham NW, agrees. In a separate interview, Mr. Armstrong criticized the new committees for keeping members away from the House floor. He objected to the idea that a member should be better informed and so better able to question the executive.

''A member should be a constituency man,'' he said. ''He should look after the people who elect him. I don't want to be an expert on everything.

''Mr. Armstrong also opposed proportional representation: ''I can't always defend the way we British do things with logic, but it is how we do them and they embody wisdom and experience.''

However, Hugh Dykes speaks for newer, younger, more active members when he calls for more resources and expert knowledge. Without them, he thinks, MPs will yield effective government to civil servants.

In his dingy campaign headquarters on Lowlands Road, Harrow, the other day he said, ''My total allowances are about (STR)7,000 a year [$11,200] for all staff, including (STR)1,500 ($2,400) for a researcher. I ask you. . . .''

Dykes is a member of the select committee on the European Common Market. ''The staff does a good job for us,'' he says, ''but senior civil servants see themselves working for ministers, not for us, and when they come to hearings it is with batteries of advisers and statistics. Every MP needs two full-time researchers, and I could use two full-time secretaries.''

Parliament sits for about 32 weeks a year from 2:30 p.m. to late at night Monday to Thursday, and on Friday mornings. Dykes says he would recommend ending daily sessions no later than 10 p.m. to avoid millions of pounds being voted by dog-tired members.

A number of members' wives, especially those whose homes are far from London, heartily agree. They rarely see their husbands during sessions, and spend their lives on trains or in cars.

Only 178 nonministerial MPs have offices to themselves, according to George Robertson, Labour MP for Hamilton. The rest share crammed cubbyholes with from two to 16 others. MPs can be seen dictating to (often shared) secretaries in corridors or the Commons cafeteria for lack of other space. And it may get worse: Until this election there were 635 members; after June 9 there will be 650.

Offices have been provided for some MPs in the Norman Shaw building in Westminster. But for most British MPs, the sort of allowances and staffs available to congressmen and senators in Washington are a distant dream.

''Common sense suggests that the provision of an office with a secretary and a researcher is hardly an exaggerated demand,'' Mr. Robertson wrote recently in the Financial Times.

Denis Healey, deputy leader of the Labour Party, points out that the Commons becomes more important if a government majority is slender. If it is substantial , as in the most recent Parliament, Parliament counts for less, he says.

Some critics say that part of the reason for the tendency toward confrontation in the Commons is the way in which government and opposition sit facing each other, rather than in the European-style semicircle of seats facing a central podium. Members rise in place after catching the speaker's eye and talk at their opponents rather than moving to a podium.

According to Christopher Jones, veteran parliamentary correspondent for the BBC, this goes back to 1547, when Edward VI allowed the Commons to meet in the long straight lines of choir stalls in a royal chapel.

''That simple act has colored British politics with confrontation ever since, '' Mr. Jones said in an interview. ''Yes, Parliament has become a talking shop.''

Mr. Jones and others say the new select committees are mainly a sop to backbench MPs, to keep them occupied. Such critics point out that 90 percent of the committees' reports are not debated by the full House. Meanwhile, they add, the party whips exert effective discipline. And backbench MPs still have little actual power.

What is to be done? Ideas suggested here include:

1. Letting television into the House of Commons, so that people can understand more about parliamentary procedures.

2. Instead of abolishing the House of Lords as an anachronism (as elements in the Labour Party would do), retain it for its experience and as a check on the Commons. Its current membership is made up of hereditary peers, appointed ''life peers,'' archbishops, and bishops.

3. Giving the select committees many more of the teeth that congressional committes have in Washington. Professor Griffith would allow them to know the current state of executive decisionmaking on major issues. The vital area for the committees is the budget: Unless they can gain real influence over how ministries make their financial decisions, effective Commons control will have to wait, Professor Griffith believes. Louis Heren urges less centralized government, more devolution of powers, and much stronger committees.

4. The Liberals and the new Social Democratic Party (SDP) want proportional representation to be introduced to make it easier for smaller parties to gain seats.

After World War II, Britain helped install in West Germany a system of proportional representation, a decentralized government, and modern trade unions. Now, Social Democrats say, it is time that Britain itself acquire all three. David Owen, a founder of the SDP and a former Labour foreign secretary, is among those who would ''bring in the carpenters'' to replace the long Commons benches with a semicircular chamber.

Others would try to soften the class system in Britain that still reserves many top establishment jobs for graduates of Eton, Winchester, Oxford, and Cambridge.

''Parliament,'' writes Louis Heren, ''inherited the divine right of kings. . . . The power of the monarch was reduced, but power was transferred to Parliament and not to the people.''

Speaker Thomas urges caution. Analysts like Mr. Heren see the need now to reexamine old ways and old attitudes to retain the valuable, discard the outmoded, and bring in the new. Next: What do British voters think are the real issues facing the country?