London — Britain asks who will lead it two years from now - a shopkeeper's daughter from Grantham, an intellectual's daughter from the left of center, a plum-voiced former Treasury chief, or a white-haired left-winger beset by strife in his own party?
The answer - closely watched by Washington and other NATO allies for clues to future British defense policies - is that the race today is between the first three. White-haired Michael Foot, leader of the Labour Party, is seen as leading a cause that today looks all but lost.
The shopkeeper's daughter, Prime Minister Margaret Thatcher, professes to see the first faint sign of hope that her mid-term slump in the opinion polls might be corrected despite 3 million people out of work and a drop in manufacturing output in December of 2.3 percent.
But the front-runners are still intellectual Shirley Williams and the man with the plum voice, political strategist Roy Jenkins. They are two of the four founder-members of the Social Democratic Party (SDP).
The Social Democrats have emerged from their just-held first constitutional conference confident that a recent slip in one opinion poll signals no serious ebb in its fortunes.
The party is coming of age fast, political analysts here say. Its convention produced spirited debate. The views of Roy Jenkins and founder William Rodgers on how the party's leader ought to be chosen were rejected. A poll of the party's 78,000 claimed members is to be held at the end of March to settle the method of selection and to decide how great a role to allow women in setting party policy.
Jenkins and Rodgers wanted the leader to be chosen by SDP members of Parliament; the party steering committee backed them. But 166 of the 305 convention delegates voted that all party members should vote on the leadership. Only 66 votes were cast for selection by MPs.
''It is going to be quite a difficult party to lead and to run,'' Mrs. Williams observed after the convention.
Roy Jenkins claimed that the SDP had ''achieved a widening appeal which stretches across the classes, the nations, and the regions of Britain and the occupational groups.'' Conservatives and Labour, he said, ''fear us far more than they fear each other.''
Both Conservative and Labour Party attacks on the SDP following the convention appear to indicate just how seriously the two mainstream parties take the SDP.
Labour Home Affairs spokesman Roy Hattersley said, for instance, they possessed only a philosophy instead of a policy, and were actually Conservatives under a ''suave veneer.''
Meanwhile, the Social Democrats face urgent problems, even as they win 30-to- 40 percent of the vote in council elections around the country. They have yet to work out details of their alliance with the Liberal Party and to decide how to hold on to 635 constituencies in the House of Commons.
A number of rank-and-file members object to making the basic party political unit an ''area'' (with up to seven constituencies) rather than the constituency itself.
SDP leaders chose the area to blunt any efforts by left-wingers at the grass-roots level to take over national party policies as happened to Labour. The SDP convention decided to keep the areas, but said local members could choose to stay with constituencies if they wished.
Mrs. Williams wants 50 percent of the policymaking Social Democratic council to be filled by women. But the convention produced a tie vote on the issue. The matter will go to the rank and file.
More fundamentally, the British electorate will soon ask for more detailed policy statements from the Social Democrats. Currently, the party firmly supports British membership in the European Community. It favors ending independent British nuclear deterrent, although it would retain nuclear weapons under NATO command. The party also favors a mixture of moderate, left-wing government spending and social planning at home.
Mr. Jenkins cannot hope to be leader of his party, let alone of Britain, unless he wins the March 18 by-election in Glasgow.
Mrs. Thatcher is working on a mild amount of government spending in her budget to be announced March 9. Unemployment will probably continue to damage her politically, however - for it is expected to stay high in 1982.
Mr. Foot is pursuing his investigation of hard-line Trotskyites and supporters of Tony Benn within the Labour Party. It was the success of the hard-left activists and of Mr. Benn in dominating various party policies that pushed Jenkins, Williams, Rodgers, and former Labour Foreign Secretary David Owen into a formal break with Labour.
Dr. Owen is also a leadership contender in the SDP.
Labour continues to do poorly at by-election polls, despite efforts to patch up quarreling between Mr. Foot and Mr. Benn.