Prime Minister Margaret Thatcher hopes to persuade President Reagan to support an international peace conference on the Middle East when she meets the President at the White House tomorrow. She will also urge him to work for a summit meeting on arms control with Soviet leader Mikhail Gorbachev before the end of the year.
On both issues her influence over Mr. Reagan is expected to be stronger than at any time since she and the President became firm personal and political friends seven years ago.
Mrs. Thatcher's talks with Reagan will be her first since she led her ruling Conservative Party to a massive victory in the general election of June 11. She will arrive in Washington having been re-elected as prime minister for the third time in a row. She now has the prospect of five more years of power ahead of her.
Thatcher is also the longest-serving leader in the Western alliance - a fact that her advisers say has persuaded her to try to use her seniority in the pursuit of a number of important foreign policy goals.
During her last major visits to Washington - in 1984 and 1986, Reagan was riding high both as a domestic leader and as a world political figure.
But Thatcher's advisers have warned her that this time the President's situation is very different.
He is enmeshed in the Iran-contra scandals. Even without the current congressional investigations, Reagan would soon fall into the category of a ``lame duck'' president. Thatcher would like to see him use his remaining influence in pursuit of an acceptable arms control agreement with the Soviet Union.
One senior British diplomat said: ``If Reagan and Gorbachev fail to meet again this year, the President may find it very hard to hold his own in tough arms control negotiations.''
The prime minister has also swung around to supporting a Middle East peace conference, and is expected to urge Reagan to look with sympathy on proposals now being pushed with increasing urgency by Israeli Foreign Minister Shimon Peres.
There appears to be only cautious optimism at 10 Downing Street about the likelihood of Reagan's being willing to give early endorsement to a Mideast peace conference. But this is not likely to deter Thatcher from pressing the point with her accustomed vigor.
The friendship between the prime minister and the President, who share a number of ideological standpoints, continues to be described by officials as close, even though there is regret that Reagan's ``clout'' has been reduced.
Thatcher's clout, meanwhile, remains considerable, not least because of her seniority as the longest-serving leader of the European Community. This enables her to exploit her influence as what one of her advisers described as ``spokesperson for Europe.''
This factor may be of great importance in the way she approaches her talks with Reagan.
In Western Europe, there is concern lest Reagan and Mr. Gorbachev try to hammer out an arms deal that runs the risk of diminishing European security.
While she presses the President to agree to an early superpower summit, she will also urge him to set limits on how flexible he may be prepared to be in his dealings with the Soviet leader.
In addition, most West European governments would like to see progress toward a Mideast settlement and many think the Americans have been dragging their feet on the issue. Thatcher's ``European spokesperson'' role will give her credibility in discussing the Middle East - not least the question of Gulf security.
Britain, along with France, West Germany, and other leading West European nations, is uneasy about Reagan's policy of reflagging Kuwaiti tankers.
Thatcher does not pretend that Britain under her leadership has once again become a front-rank nation, in the sense that the United States and the Soviet Union clearly are. On the other hand, her long experience as a world leader seems to have given her considerable potential leverage.
One foreign policy adviser remarked: ``Mrs. Thatcher remains in the ascendant, while President Reagan's star is waning. In the next year or so, she can hope to take on more of the burden of Western leadership.
``This week's Oval Office talks will see her at the peak of her influence in world affairs.''