LONDON, JUNE 9 -- At age 36, Paul Boateng has all the right credentials for election to Parliament. A lawyer by training, he has done his time in local government and community service. Listed in Britain's Who's Who, he is married to a social worker, has five children and is a member of the board of the English National Opera.

The fact that Boateng's family tree reaches into Africa seems incidental to his political record and high standing in the Labor Party.

Yet, when the votes are counted after Thursday's general election, Boateng is likely to attract instant fame as one of the few blacks ever elected to the House of Commons.

A record 27 nonwhites, including blacks and Asians, have been nominated for seats in Britain's 650-member Parliament this year by the three main political parties. Boateng has the surest chance of all, seeking election in a London district that Labor last won by more than 10,000 votes, while at least two and possibly as many as four other nonwhites are expected to win seats.

That number falls far short of equal representation for nonwhites, who make up 4.5 percent of Britain's 56 million population.

Although the post-World War II decades brought waves of immigrants from Britain's once vast empire in Africa, Asia and the Caribbean, the Mother of Parliaments has remained virtually a whites-only club. Three Asians have held seats, the last elected in the 1920s.

That Britain has had difficulty adjusting to a multiracial society can be seen in the 1986 British Social Attitudes Report compiled by the government-approved Social and Community Planning Research Institute.

According to the report, 90 percent of British adults see their society as racially prejudiced against blacks and Asians, 30 percent described themselves as racially prejudiced and a majority of the country thought the racial situation would get worse in the future.

At the same time, many sociologists point out that the historically low economic status of nonwhite immigrants and the feeling of many, especially in the Asian community, that they would some day "go home," tended to limit their desire to participate in politics here.

The conventional wisdom in Britain has been that nonwhite candidates simply could not capture enough white votes to win.

Although they have previously been nominated by the major parties -- five in 1979 and 18 in 1983 -- they were only for "throwaway" seats in districts where the nominating party had no chance with any candidate. But demographics and a rising sense of their own political power, particularly among blacks, have begun to change the equation.

According to Britain's 1981 census, 52 English districts now have what sociologists call "NCWP" (New Commonwealth and Pakistani) populations of 15 percent or more. In some districts, concentrated in London and the West Midlands, the nonwhite total is between 30 and 50 percent of the population.

Beginning in the early 1970s, nonwhites began moving up the economic ladder and becoming active at the political entry level, where more than 300 now hold elected seats on local and municipal government councils.

"Black people have started getting into the white-collar jobs like law and politics," said a British-born computer programmer here, the son of Jamaican parents. "It's the only way. It's the way it happened in the States, and it's got to happen here."

Some experts believe that, as nonwhites continue to rise up the economic ladder, they will be attracted to the Conservative Party of Prime Minister Margaret Thatcher.

But a vocal Conservative minority considers nonwhites alien to British culture and at annual party conferences has introduced long lists of proposals calling for "repatriation" of immigrants.

Studies indicate that more than 80 percent of nonwhites still vote for Labor -- as much because it is considered the "party of the working class" as for its attitudes on race.

"I'm doing well now, and I agree with some of Thatcher's policies, particularly the financial ones," said the computer programmer. "But I can't see voting for the Conservatives. I've been down before, and I do have a conscience. I know what it's like."

As in the United States, the integration of blacks into the traditional party structure has not been a smooth process.

Impatient for political power long denied them, black activists have pressed the Labor hierarchy to incorporate their concerns into the mainstream party program.

For the past several years, a battle has been raging between Labor leader Neil Kinnock and advocates of so-called "black sections" with guaranteed seats on party governing boards. Kinnock has rejected these separate groupings for blacks and has described them as segregationist. In response, the more militant among black leaders have publicly labeled the party itself as racist.

Of the 27 nonwhite candidates, 14 are from the Labor Party, with six Conservatives and seven from the third party, Alliance.

Among those seen as having a chance of winning, all are Labor candidates running in districts with large nonwhite populations.

In addition to Boateng, they include Diane Abbott, a 33-year-old Cambridge University graduate running in the London district of Hackney North, and Bernie Grant, a 43-year-old Guyanese immigrant who has worked as a railroad clerk and currently is the local council leader in the London borough of Haringey.

Abbott and Grant are outspoken advocates of minority rights and "black sections," and both have been singled out by the Conservatives as dangerous militants.

But whatever their differences with their own Labor Party, they and other black candidates have toned down complaints during the campaign.

Once in Parliament, says Grant, "we will be raising issues which affect black people only . . . racism and racial disadvantage." For the moment, however, "getting Labor into government" is the "overriding interest."