London — Latest signals here are that President Reagan's staunchest ally in Europe will face the voters again in June, and not in October as many have predicted. ''The pressure is increasing for June,'' one reliable government source confirms.
The United States and NATO have a big stake in the outcome. Prime Minister Margaret Thatcher, well ahead in the opinion polls, strongly supports the alliance and its decision to install medium-range missiles in Europe unless Moscow dismantles its own.
Her chief opponent, Labour's Michael Foot, lags in the polls, but hopes to turn unemployment and recession to his advantage. If he wins, he is pledged to give up Britain's nuclear deterrent, raising questions about British standing within NATO.
Conservative members of the House of Commons are telling the prime minister she should not wait until October because:
* Latest opinion polls give her a lead over Labour of between 8 and 18 percent. Her supporters say she should strike before voters forget about the Falklands victory.
* By June, electoral boundaries will have been redrawn here, and the Tories stand to gain at least 15 seats. The Labour Party is challenging the commission's work, and must decide soon whether to carry its challenge to a final appeal.
* Early elections would help prevent Labour ditching Foot, whose image is not that of a forceful leader, and choosing a more telegenic figure, such as Peter Shore.