Begin pursues his hard line, defies friends and allies; British-Israeli diplomatic dispute over Jerusalem seen to reflect cooling relations between the two countries

The latest evidence of a deteriorating relationship between Britain and Israel erupted recently in a contretemps between British Foreign Secretary Lord Carrington and Israeli Prime Minister Menachem Begin.

The issue, seemingly a small one, was fraught withe diplomatic significance. It began with a question put to the foreign secretary during an interview on Israeli television July 11. He was asked about Mr. Begin's controversial plan to move the prime minister's office from West Jerusalem (recognized as Israeli territory) to East Jerusalem (annexed by Israel but still generally considered as the Arab sector).

Lord Carrington, echoing the condemnation of the plan by a number of countries including the United States, replied that it would be "a great mistake if your prime minister moves there."

"I think it will make things more difficult for your friends," he added, "and very much easier for your enemies."

His remark, which government officials here insist is in line with British foreign policy through the years, sparked a tart retort from Mr. Begin. In his first public statement since entering a hospital two weeks ago, Mr. Begin pointed out that it was not Lord Carrington's business "to advise the prime minister of Israel where his office should be in Jerusalem, the capital of Israel."

Behind Mr. Begin's acerbic remarks -- which observers here describe as an "unprecedented" rebuff between two ostensibly friendly nations -- lie a number of issues:

* On July 9, Lord Carrington told the House of Lords that "Our fundamental commitment to Israel does not and cannot extend to her actions as an occupying power." His speech was criticized by Foreign Minister Yitzhak Shamir, who accused Britain of seeking to win Arab hearts by deserting Zionism.

* Previously, Mr. Begin had upset Europeans by accusing them of failing to act strongly enough to preven a remark that the British ambassador to Israel, John Robinson, publicly criticized as highly offensive to many British citizens.

* Most keenly felt, however, is the sense that Britain was behind the European Community (EC) declaration at Venice June 13, which said that the Palestine Liberation Organization (PLO) "will have to be associated with the negotiations over the future of the Middle East."

No one anticipates a break in relations between the countries, which shared nearly L500 million ($1.175 billion) in trade in 1979. But together, the tiffs reflect what Geoffrey Paul, editor of the influential Jewish Chronicle, calls "a general unhappiness with the British attitude of late."

Mr. Paul told the Monitor that British foreign policy is, in his view, "more critical of Israeli policy than it was three years ago," when Britain's Labour government still basked in the warmth of a sunny Anglo-Israeli relationship built up by former Prime Minister Harold Wilson.

Publicly, the Conservative government promulgates what Lord Carrington calls an "evenhanded" policy of support for arabs and Jews alike. Privately, however, many see the British Foreign Office as leaning Arab-ward.

But so complex are Anglo-Israeli and Anglo-Arab realtions here -- with Prime Minister Margaret Thatcher herself, for example, representing a constituency with a strong Jewish vote -- that few see any prospect that the Foreign Office would dump Israel to curry Arab favor.