London — Overlooking the waters of the Thames in a corner of the glorious neo-Gothic profusion known as the Houses of Parliament is a comfortable living room almost directly beneath Big Ben.
In it a gentle, unassuming man in a dapper suit and waistcoat pours a cup of tea and neatly slices a piece of cake.
As he hands both to a visitor with a murmur of welcome, it takes an effort to realize that apart from royalty, only five others in the entire United Kingdom rank higher than this quiet man.
Bruce Bernard Weatherill, known all his life as Jack (his twin sister Margery is known as Jill), is a former master tailor to royalty who still carries a thimble in his pocket at his mother's request ''to keep me humble.'' For four years he sat cross-legged on a workroom floor as a tailor's apprentice, specializing in riding breeches.
He also happens to speak Urdu from his years with the 19th Bengal Lancers in World War II. And today he is the 134th Speaker of the world's preeminent parliament, the House of Commons.
Speaker Weatherill, whose opening cry of ''Order! Order!'' is heard around the country in daily radio broadcasts of Parliament, is also at the center of a lively national debate about maintaining that order and discipline on the floor of the House of Commons itself.
The debate has wide ramifications. ''Bitterness in the Commons can sour politics in the country,'' says Peter Riddell, political editor of the respected Financial Times newspaper.
Keeping order is a stern test for a man who never dreamed he would occupy such an exalted position. He was elected to the elaborate Speaker's chair only last June and must carve out his own style and presence in the shadow of the previous Speaker, George Thomas, who is regarded as one of the most effective holders of the office in modern times.
Unlike the Speaker of the House of Representatives in Washington, the Speaker in Westminster is strictly impartial. He presides over 726 years of tradition: The first man to lead the House was Peter de Montfort in 1258.
Surrounded by ceremony and deference and clad in a full-bottomed white wig and black robes, he wields final authority in his own domain.
He may not speak in debates himself, but only he can decide who else can take the floor. He must know the names of all 650 members and each must try to catch his eye.
The whole House elects him, rotating the office between the major parties. Mr. Weatherill is a Tory; Mr. Thomas, now Lord Tonypandy, is a Labour man.
Some in the house and in the national press think Mr. Weatherill shows insufficient firmness to keep the house disciplined.
But ''it would be wrong to be too hard on Mr. Weatherill,'' Peter Riddell notes in the Financial Times.
Friends made in a 20-year house career as member, whip, and deputy speaker say he is utterly fair and devoted to upholding the reputation of Parliament.
Expert onlookers like Mr. Riddell and a number of MPs acknowledge he is having to deal with unprecedented rivalries and frustrations of four separate parties in a political system designed for only two.
The Labour opposition, led by the relatively young, ambitious, and outspoken Neil Kinnock, is frustrated at the size of the current Tory majority (about 140 seats). The still-new Social Democrats, who won almost 26 percent of the vote last June but only six actual seats, demand that the Speaker call on their members in each debate.
The Liberals, with 17 seats, are equally concerned with their own prerogatives. And 96 restless new Tory backbenchers, swept in by the Thatcher landslide last year, also clamor to speak in debates.
Lately the floor has seen a number of boisterous scenes, which sound even worse when broadcast on radio. They culminated Feb. 23 in highly publicized episodes later described by a Tory member as ''disgusting clamor'' and ''moronic uproar.''
Long parts of the prime minister's question time were drowned in shouting. A new Labour member jostled a Social Democrat in trying to sit on an opposition bench. The prime minister was challenged by Mr. Kinnock, who in turn provoked a heated interjection by the Social Democratic leader, Dr. David Owen.
The next day, Speaker Weatherill firmly appealed for an end to such behavior. After defending ''robust debate'' but warning that it did not extend to ''disruption,'' he was cheered by many members who think recent disturbances have gone too far.
How does the Speaker himself see the house he both leads and serves?
At the end of a busy week in the chair, he spoke with affection and respect of the chamber and its members.
''Our system is one of controversy politics,'' he observed. ''Actually, the behavior of the house is very much better than it has been in history. There never was a Golden Age here, you know. . . .
''I am positively in favor of robust debate, as I've said. . . . The quality of the members is very high. It is their duty to hold the government to account.''
The Speaker agreed that this parliament was ''difficult.''
He has won praise for making sure that as many backbenchers as possible speak in debates, and he agrees with the Conservatives' Leader of the House, John Biffen, who says Parliament is doing no more and no less than it has always done.
''What I'm doing,'' the Speaker went on, ''is bringing the speakership into the context of the age. In a modern school, the headmaster cannot rely on the cane; I don't seek to do so in the house. In the 1980s, other methods of ensuring discipline have to be used. . . .
''I have relatively few points of order raised with me on the floor because I work behind the scenes to iron out frustrations and difficulties. We don't want public rows if they can be privately solved.''
Whereas Mr. Thomas was a definite Establishment figure, Mr. Weatherill is more of a backbench than a ministers' man.
His ''heart is in the right place,'' says Michael White, who covers Parliament for the Guardian newspaper. He has ''tried to take the stuffiness out of the job. . . . It is difficult in an age which lacks deference . . . (but) it is early days.''
A few days later the Sunday Telegraph newspaper carried a column commenting favorably on Weatherill's crisp private manner and his ''good line in jokes directed firmly at himself.''
The best-known of these anecdotes: Newly elected to the House in 1964, he overheard one richly aristocratic voice saying to another, ''I don't know what this place is coming to, Tom; they've got my tailor in here now.''
Weatherill likes to use a metaphor from his own past experience.
''The Speaker's job is like riding a horse. Success in the saddle is a neat combination of sensitivity and command. The successful rider is one with the horse. A successful Speaker is one with the house.''
He is seeing more support on the floor for his efforts to keep order.