LONDON — Acknowledging bitter divisions within his Conservative Party and his cabinet over Britain’s role in Europe, Prime Minister David Cameron told Parliament on Tuesday that he would allow government ministers to campaign for or against remaining in the European Union in a referendum that could take place as early as this summer.

Cameron favors remaining in the European Union if he can get some relatively modest changes to his nation’s relationship with Brussels, in particular protection for countries not using the euro and some restrictions on benefits for new immigrants who come to work in Britain.

But some of his key cabinet ministers and other party figures, including Foreign Secretary Philip Hammond, Home Secretary Theresa May, and Mayor Boris Johnson of London, are known to have doubts about Britain’s membership in the bloc, although they have remained noncommittal about their positions on the referendum.

Three additional ministers, Iain Duncan Smith, the work and pensions secretary and a former party leader; Theresa Villiers, the Northern Ireland secretary; and Chris Grayling, the leader of the House of Commons, are believed to oppose British membership in the union and are said to have threatened to resign if Cameron required that his entire cabinet speak with one voice on the issue.

Addressing the House of Commons, where he has a majority by only 12 seats, Cameron said that after he finishes his negotiations with his EU partners over a new relationship for Britain with the bloc, “there will be a clear government position,’’ which is expected to favor continued membership.

“But it will be open to individual ministers to take a different personal position while remaining part of the government,’’ he said.

An aide to Cameron who was not authorized to speak publicly said the prime minister’s decision recognized “the political reality within the Conservative Party,’’ where a significant minority of lawmakers favors Britain’s exit from the union.nisters to speak their minds.

Cameron’s decision goes against the advice of some prominent Conservatives, including former Prime Minister John Major and Michael Heseltine, a former government minister, that he should insist upon the usual principle of collective responsibility.

Government officials have been hinting strongly that after another European Union summit meeting in mid-February, Cameron will call the referendum as early as June or July, so that the campaign is affected by another summer of chaotic migration from the Middle East into Europe. Cameron has pledged to hold the referendum by the end of 2017.

Cameron is following the lead of Harold Wilson, a Labour prime minister, who also allowed his cabinet their personal views before Britain’s previous referendum, in 1975, on whether to stay in what was then the European Economic Community. This time, Labour is expected to favor remaining within the European Union.