Britain is considering a diplomatic initiative to try to speed peace negotiations in the Middle East through international recognition of the Palestinians' right to self-determination in return for Palestinian acceptance of Israel's right to exist.

British diplomats are considering an addition to U.N. Resolution 242, which now calls on Israel to withdraw to its borders that existed before the 1967 Arab-Israeli war. The new clause would advocate Palestinian self-determination as part of a "comprehensive" settlement.

In return, the Palestinians, including the Palestine Liberation Organization, would be expected at least implicitly to recognize Israel by accepting the resolution's existing "acknowledgement of the sovereignty, territorial integrity and political independence of every state in the area and their right to live in peace within secure and recognized boundaries."

The British aim, according to informed sources, is to draw the Palestinians and Jordan into the lagging negotiations between Egypt and Israel on limited Palestinian autonomy in the Israeli-occupied West Bank and Gaza Strip as provided in the Camp David peace agreement.

The sources said British Foreign Secretary Lord Carrington has become convinced by his talks with Arab leaders since the Soviet invasion of Afghanistan that a rapid solution to the Palestinian problem is essential to achieving stability and protecting vital Western interests in the Middle East and Southwest Asia.

Although British officials insist that no final decisions have been made to go ahead, either alone or with the help of the other European Common Market countries, the Israeli government has already reacted angrily to reports it has received about British intentions. Israel strongly opposes any change in Resolution 242 that would even imply that the Palestinians have a right to an independent state on Israel's border.

For this reason, special U.S. ambassador Sol Linowitz, who is participating in Israeli-Egyptian negotiations on Palestinian autonomy, asked Carrington in a meeting here three weeks ago to delay doing anything until Linowitz had time to make more progress in the talks before their May deadline. Carrington and U.S. Secretary of State Cyrus Vance are to discuss the subject further Thursday in their consultations here on the Afghan crisis.

Israeli Prime Minister Menachem Begin used his farewell meeting with outgoing British Ambassador John Mason this week to object in strong language to the evolving British policy on the Palestinians.

Carrington signaled the intentions of Prime Minister Margaret Thatcher's new Conservative government when addressing the United Nations last September, shortly after an unsuccessful effort was made there on the PLO's behalf to amend Resolution 242. Carrington said then that the resolution, which the British had helped draft, was "incomplete" in treating the Palestinians only as a "refugee problem" to be solved along with an Israeli withdrawal to its pre-1967 borders.

The resolution "takes no account of the legitimate political rights of Palestinians, which go well beyond their status as refugees," Carrington said in September. "Nor does it take any account of the Palestinians' belief that they are a separate people with right to their homeland."

"This I believe is an area in which Resolution 242 may be supplemented," he proposed then, "not, I emphasize, replaced, amended or distorted, but supplemented to meet this point."

British officials believe the Camp David agreement alone cannot solve the problem and that the Linowitz negotiations, do not appear likely to produce significant results before the May deadline for a West Bank and Gaza autonomy plan. Furthermore, the British doubt that the Carter administration will be able to do much more during an election year, especially if it involved approaches to the PLO that would antagonize Jewish-American voters.

These circumstances could open the way for a British or British-led Common Market initiative on the Palestinian question in the United Nations, according to sources, although they say British officials do not want to rush ahead with anything that might jeopardize the autonomy talks. At the same time, they believe Britain could help rescue the talks, despite Israel's objections, by acting before the May deadline.