London — Britain is spearheading a NATO crusade against the idea that giving up medium-range missiles is the best way to ensure peace. The campaign, ordered by President Reagan's strongest supporter in Europe, Prime Minister Margaret Thatcher, comes on the heels of the European visit by Vice-President George Bush.
It reflects a growing awareness at 10 Downing Street that, with cruise missiles due to begin deployment in Britain at the end of this year, the idea of NATO's giving up its planned deployment of new nuclear weapons is widely championed by vocal groups of young people, women, churches, socialists, communists, labor unions, and other segments of the European peace movement.
British officials acknowledge that ''we still have a lot to do'' to win the public-awareness battle. Comments one: ''The Falklands war preoccupied us for a long time last year and we lost ground to the peace groups. But we are back on the track now.''
The latest opinion poll here, conducted by Opinion Research for the commercial television network, showed 47 percent opposed to the arrival of cruise missiles in Britain and 39 percent in favor. On the other hand, the poll showed 78 percent against unilateral disarmament.
Even as 150 peace activists from 19 countries met in Yorkshire to hammer out strategies for the rest of 1983, the British government rolled out a campaign which also foreshadows a major government plank in the next election.
* The prime minister herself moved onto the offensive with a characteristically uncompromising speech against unilateral disarmament to the annual conference of the Young Conservatives at Bournemouth. If Hitler had had nuclear weapons, she said, and the West had given them up, Germany would have had the chance to blackmail mankind.
* The newly appointed defense secretary, Michael Heseltine, defended the system of joint US-British control of the US bases in Britain at which cruise missiles are to be deployed. He spoke at length on a national television program Feb. 13.
* Former Prime Minister Lord Home, who was parliamentary private secretary to Prime Minister Neville Chamberlain at the time of Munich in 1939, told the Young Conservatives that ''the lesson of this century is clear. If a first-class power threatens the peace, it is necessary to combine the power of the United States and Western Europe. Only both will do.''
* Conservative Party chairman Cecil Parkinson repeated the theme that in his view, today's unilateral disarmers bring to mind the well-meaning appeasers of Hitler in the 1930s.
* Meanwhile, peace groups in Britain note with concern a growing number of pro-nuclear deterrent groups speaking out against them. They range from new publications opposing the unilateralist cause from the Arms Control and Disarmament Research Unit of the Foreign Office to a Committee for Peace With Freedom chaired by Winston Churchill, grandson of the wartime prime minister and himself a Conservative member of Parliament. Mr. Churchill has been asked by the Conservative Party to speak out in public with the title of ''coordinator'' for multilateral disarmament (everyone disarming together) and defense.
The British Atlantic Committee and other pro-alliance groups are also paying more attention to countering unilateralist arguments.
The left-of-center New Statesman weekly magazine recently listed various anti-unilateralist groups under the headline, ''Tories wage secret war on peace campaigners.''
The prime minister showed in her own speech that she is giving considerable thought these days to the influence and publicity represented by the peace movement. She cited in her speech what she called ''five myths'' of the unilateralists' argument:
1. Nuclear weapons were so terrible that Britain should have nothing to do with them. But, she said, that would allow the Soviets to blackmail the world, as Hitler would have done.
2. The belief that Moscow does not want war. How, she asked, would that translate into Hungarian, or Czech, or Polish?
3. The belief that it is moral for Britain to give up nuclear weapons and still rely on the Americans to defend it.
4. By having no US bases, Britain would cease to be a target for Soviet missiles. ''Just look at a map,'' she said, indicating Britain's strategic location.
5. ''Defenselessness prevents attacks.'' Look at Afghanistan, she suggested, and the notion is disproved.
Mr. Heseltine once again rejected demands here for a ''dual-key'' method of preventing the US from using cruise missiles at will - that is, Britain and the US each possessing an electronic ''trigger.'' Both would have to be activated before a missile could be fired. The US had offered dual-key, but the British government had rejected it, he said. It would cost (STR)1 billion ($1.5 billion) to make possible, and that was just too much.
Besides, he went on, existing arrangements for ''joint decisionmaking'' on the use of American bases meant that no cruise missiles could be fired without the consent of the British prime minister. British servicemen would be needed to load the cruises onto mobile launchers and disperse them around the countryside if a war alert came.
Critics say that a Soviet missile would take only a matter of minutes to reach Britain and that the arrangements apply to an earlier, less lethal time. Many critics urge the dual-key policy.
The Campaign for Nuclear Disarmament peace group, and the opposition Labour Party, have both criticized the prime minister for her allusions to Hitler appeasers.