DIPLOMACY : Major’s Get-Acquainted Visit With Clinton Is a Critical One : The Tories’ ties to Republicans may shadow the encounter.

British Prime Minister John Major flies to Washington next week on a critical mission to size up a new American President.

Major, who was on close terms with former President George Bush but has never met Bill Clinton, needs to establish the kind of personal friendship that has generally marked the special relationship between Washington and London.

His get-acquainted visit will be made no easier by the fact that President Clinton is the first Democrat in the White House in 12 years, a period during which the Conservative Party, traditionally cozy with Republicans, has been in command here.

Reports from Washington suggest that Clinton was angry that the Conservatives’ London headquarters sent a couple of functionaries to Washington during the U.S. presidential electioneering to advise Bush’s faltering campaign.

Some of the Tory leaders, in turn, are unhappy over word from the United States that Clinton may send a special envoy to Northern Ireland to report on the long-running sectarian conflict in that British-ruled province.

Further, Major arrives in Washington at a moment when his leadership is being widely questioned because of his failure to grapple successfully with the ailing economy and his wavering position on ratifying the Maastricht Treaty, the European Community’s agreement on political union.

Thus Major is arriving in Washington not at the top of his form, a flawed partner in an uncertain transatlantic relationship.

The two leaders are expected to cover a wide range of subjects when they meet at the White House on Wednesday: the world economy, trade and tariffs; Russia; the fighting in Bosnia-Herzegovina, and European Community issues.

On the subject of Bosnia, Major is expected to outline for Clinton the reservations widely held among European leaders about getting deeply involved militarily in the turbulent Balkans.

On the touchy subject of Tories aiding the Bush campaign, a top Major aide declared heatedly: “We will certainly try to get across the difference between No. 10 Downing Street--that is, the prime minister’s office--and the Conservative Party Central Office.

“Our view at No. 10 of the party’s election campaign is unprintable, and the idea of them telling someone else how to conduct a winning election campaign is really laughable. We won last spring despite the campaign.”

Major is reported to be less upset about the possibility of an American envoy going to Northern Ireland than are some of his fellow Conservatives--and the Ulster Protestants.

“Our reaction to an American emissary depends on who it is and how he goes about it,” said the Major adviser. “If someone wants genuinely to assess a complicated situation, we would be happy to sit down and explain it.

“We are all working to get the dialogue going again between north and south, Protestant and Catholic.”

Major has spoken by phone with Clinton three times since the latter was elected President, and officials at No. 10 are hopeful that the two leaders will hit it off in Washington.

“They are about the same age,” a British official pointed out, “and they come from roughly the same background, sharing much of the same outlook, so there’s no reason they shouldn’t get along.

“While it is true that the relationship between old friends like Britain and the United States should not depend only on a friendship between their current leaders, there’s no question but personal contacts are quite important,” the official continued.

“The Gulf War demonstrated that. It will be extremely valuable for Major and Clinton to get to know each other, trust each other, feel sure they can depend on one another--and follow through on agreements.”