President Reagan arrived here today for a visit intended to provide rest and to polish his image between economic and military summits, but the stop has been transformed by the Falkland Islands crisis into a test of the special relationship between Britain and the United States.

As the final stage of the fighting in the South Atlantic appears imminent, Reagan and Prime Minister Margaret Thatcher are to continue discussions they began Friday in Paris, before the seven-nation economic summit at Versailles, about what will happen to the Falklands after Britain's expected military victory. Reagan and his advisers are continuing to try to persuade Thatcher to seek an accommodation with Argentina about sovereignty over the islands, according to informed sources here, while Thatcher is planning instead to give them eventual independence.

Reagan arrived here tonight after a tiring day in which he left France early this morning and traveled with Italian Prime Minister Giovanni Spadolini to Rome. Once there, the president went to the Vatican to meet with Pope John Paul II. Details on Page A13

Reagan and his wife Nancy were greeted at Heathrow Airport by Thatcher and Prince Phillip, the husband of Queen Elizabeth II. Afterward, the Reagans left immediately for Windsor Castle to meet the queen and Prince Charles, the heir to the throne. According to a spokesman for the palace, the queen then entertained the president at a "very small dinner, 38 people in all."

U.S. officials had hoped that Reagan's stay in Britain, which is dominated by events offering easy access for the media, would help enhance the president's image in Europe. That has become clouded, however, following the controversial U.S. vote at the U.N. Security Council on a resolution calling for a cease-fire in the Falklands. The United States originally voted against the resolution, but Ambassador Jeane J. Kirkpatrick later said orders to change the U.S. position to an abstention were delayed and reached her too late. Much of the British press has strongly condemned the U.S. foul-up.

Government sources here said British forces on the Falklands would not delay their decisive assault on Stanley because of Reagan's 41-hour visit here. With British troops now completely surrounding the Argentine occupation forces around Stanley, the sources said, beginning the attack is now a military rather than a political decision.

The commander of British forces on the Falklands, Maj. Gen. Jeremy Moore, today broadcast a radio appeal to the commander of the Argentine garrison at Stanley, Brig. Mario Menendez, asking him to tell his men to lay down their arms because their position has become hopeless. "Let's end the killing," Moore said, using a Spanish speaking Marine captain as an interpreter. The Defense Ministry here said it had no information about any reply from Menendez.

During heavy artillery exchanges in recent days, British troops have moved to within only a few miles of Stanley and consolidated their positions for the final push, according to military sources here and British correspondents on the Falklands.

British Marine commandos and Gurkhas killed 60 Argentine soldiers as they advanced from the forward British headquarters on Mount Kent, seven miles from Stanley, toward a retreating outer ring of Argentine defenders, military sources said. Many Argentine positions on foothills between Stanley and Mount Kent were abandoned without a fight, British correspondents reported.

The British forces also completed their land encirclement of Stanley by moving to high ground north of Stanley across its harbor from the airport, enabling British guns now placed there to join those on the heights west of Stanley in the continuous shelling of Argentine positions and to ensure that the airport is not used by the Argentines to resupply their forces. British officials said they did not know what casualties Argentine troops have suffered from this heavy shelling and the accompanying naval bombardment from British warships in waters east of Stanley.

After what he had called operations of "extraordinary daring" to move troops and their equipment into position in continuing stormy weather, British television correspondent Michael Nicholson reported tonight that the Royal Marine commandos who "outflanked the Argentines north of Stanley" are now moving "freely along the northern waters of East Falkland." He did not disclose whether they moved there by air or water, but he said that heavy cloud cover protected them from Argentine observation or air strikes.

The Defense Ministry said here tonight that Argentine Canberra planes bombed British forward positions on the slopes of Mount Kent twice in recent days but did not cause any casualties. British correspondents on the Falklands said another Canberra was shot down attempting to bomb the main British ground base at San Carlos.

British forces have secured all of East Falkland except Stanley, where up to 7,000 Argentine troops are believed to be dug in. But correspondent Nicholson said British forces have resumed shelling Argentina's remaining garrisons at Fox Bay and Pebble Island on West Falkland because of worries that the estimated 1,500 troops there might be reinforced from the mainland.

Thatcher said last week, in ruling out any negotiations with Argentina or a cease-fire without a complete Argentine withdrawal amounting to surrender, "I admit I don't want those islands ever to be handed over to Argentina."

Her attitude has caused concern within the Reagan administration, although the president has been careful not to reveal it. Thatcher's aides also insist that she is just as eager as U.S. officials to achieve cessation of hostilities and restore stability in the South Atlantic after the Falklands are recaptured but that public opinion would not now allow a deal with Argentina.

"The change in attitude in this country toward the long-term future of the Falklands hasn't perhaps registered with the U.S. administration quite as strongly as perhaps it will over the next two or three days" during Reagan's visit here, Cecil Parkinson, chairman of Thatcher's Conservative Party and a member of her inner "war cabinet," said on British television yesterday.

"The people of this country are quite determined that if we have to lose lives and incur this enormous expenditure in regaining our territory because Argentina simply would not negotiate a peaceful settlement," Parkinson said, reflecting Thatcher's view, "we are just not prepared now to hand those islands over in any sort of foreseeable future. That is an option that has been closed."

This view also appeared to be supported by a new national opinion poll, in which only 3 percent of the respondents favored negotiating a sovereignty deal with Argentina. The option receiving the most support was Thatcher's proposal for economic development, population growth and eventual independence for the Falklands, with their security protected by a multinational force.

U.S. officials fear this would leave the Falklands a festering sore in the South Atlantic, subject to periodic military raids by Argentina, that will make it impossible for Britain and the United States to restore good relations with Argentina and other Latin American countries.