Britain tries to patch holes in the alliance

The Western alliance is stronger than many of its critics believe, but still beset with problems which lend encouragement to the new Soviet leadership.

That is the broad message American Secretary of State George Shultz is to hear as he ends his first official tour of Western Europe in London Dec. 16-18.

Britain, whose Prime Minister Margaret Thatcher supports the basic Reagan strategy toward the Kremlin, is generally encouraged by the low-key nature of the Shultz meetings on the European continent.

''The trip has been singularly quiet,'' comments one authoritative source, ''and I take an enormous amount of comfort from that. . . . His talks have gone rather well. . . . It has been positive and helpful to see so little controversy in the headlines.''

The US-French agreement Dec. 14 on a program to achieve a common economic strategy toward East-West trade is taken here to indicate that relations between Washington and Paris are improving. It was France that dissented when President Reagan announced Nov. 13 that a formal allied policy document had been hammered out and that because of it, he was lifting US sanctions against European companies supplying the Soviet natural gas pipeline.

Diplomatic sources here say that details of a joint allied economic approach to Moscow remain to be agreed, but they believe the general atmosphere within the alliance has taken a turn for the better.

Mr. Shultz finds here a government which has just boosted its defense spending to make good losses incurred in the Falklands campaign against Argentina. About (STR)3 billion ($4.8 billion) is to be spent between now and 1985-86 for new ships, for the garrison on the Falklands itself, and to buy Phantom jets and Chinook helicopters from the US.

Not only will this help make British forces more mobile, but the money comes on top of an existing commitment to NATO to boost defense spending by 3 percent a year in real terms between now and 1986.

Meanwhile, Britain will tell Mr. Shultz it is seriously concerned that the growing peace movement is playing into Soviet hands.

Britain supports President Reagan's desire to counter the peace protests against the 572 cruise and Pershing II missiles due to be deployed by 1984 against Soviet SS-20, SS-4, and SS-5 missiles in the western USSR.

As long as Margaret Thatcher remains prime minister, Britain will honor its pledge to take its share of cruise missiles. But Mrs. Thatcher is so concerned at the way the idea of unilateral disarmament is being supported in this country , that she has privately urged her Cabinet to speak out much more strongly against it.

As seen from here, hardly a day will go by in 1983 without the political left and European communist parties floating new ''scare'' stories designed to block cruise and Pershing deployment at almost any cost.

These stories will be hard for governments to combat, since officials and protestors alike favor peace. But Mrs. Thatcher has made it clear that the ability to make a persuasive public case for NATO nuclear strategy will be a prime requirement for the candidate she is about to select to replace John Nott as British defense secretary. Mr. Nott is retiring from politics.

The peace movement is one of four major problems for the government next year , officials agree. The other three: the economy, Britain's strained relations with (but commitment to) the European Community, and law and order.

Mr. Shultz will be told here that the government is unimpressed with the apparent Soviet offer to reduce its intermediate-range missile strength by one-half if the US will forgo cruise and Pershing deployment. ''The Soviet Union is prepared to cut its superiority in half,'' comments one senior source. ''Yes, that's a move in the right direction, but now is not the time to weaken. Let's get more.''