London — With US Secretary of State Alexander Haig saying ''time is slipping away from us,'' two main issues dominated last-minute, intensive diplomacy here to find a solution to the Falkland Islands dispute.
The first issue was whether the British flag could once again fly over the islands even while allowing Argentina a face-saving way of moving on to the next stage of talks--the long-term future of the Falklands.
The second was how to discover what the 1,800 islanders themselves want for the future, since London has repeatedly declared that their wishes must be taken into account. A lively debate over what the islanders really feel has begun here. No one knows for sure.
One urgent need late April 12 was more time for talk. Clearly, London had not heard anything from Argentina to cause it to call off the British naval task force or to agree to any kind of truce as suggested by Peru (and reportedly accepted by Argentina).
At the end of a marathon 11-hour negotiating session between Mr. Haig and Prime Minister Margaret Thatcher at 10 Downing Street, signs were mixed.
On the one hand, no shots had been fired in the South Atlantic and Mr. Haig was flying back to Buenos Aires.
On the other, Britain was apparently not prepared to allow Argentina to keep its flag flying over the islands while an international peace force took over.
Mr. Haig confirmed before leaving for Argentina that he had brought ideas to London and they had been discussed in considerable detail. He said:
''We made some progress, but a number of substantial difficulties remain. So we will be returning this evening to Buenos Aires as time is slipping away from us on this subject.''
He refused to discuss details of the talks. But, reportedly, one of the ideas discussed would trade a withdrawal of Argentine forces from the Falklands for an about-face by the British naval task force and British agreement to compromise on sovereignty. Mrs. Thatcher is thought to have been prepared to agree to most of the package but insists that she cannot compromise on the central issue of reasserting British sovereignty.
British Foreign Secretary Francis Pym indicated that Britain was standing firm when he said issues had been explored ''very carefully but differences remain.'' He added: ''We are both very anxious to resolve this problem by peaceful means.''
Both Mrs. Thatcher and Mr. Pym must report on the state of the dispute to a recalled House of Commons April 14. That provides one new deadline pressure - as does the continued steady approach of the British fleet, whose initial elements are already enforcing the 200-mile blockade around the islands.
As part of the Haig mission, United Nations Secretary-General Javier Perez de Cuellar was reported by Monitor correspondent Louis Wiznitzer to have received a telephone call from Mr. Haig and broken off a European tour to return to New York. This raised the prospect that a UN peacekeeping force might be imminent.
Some British sources, including former Foreign Secretary David Owen, were encouraged that both sides were negotiating.
A number of politicians and analysts say the time has come for the future of the islands to be settled at last. Talks have dragged on between Britain and Argentina for almost two decades. It makes sense for Argentina to have a formal, defined role, since the islands are so close, it is said, while allowing the islanders to keep as much of their British way of life as possible.
Foreign Secretary Francis Pym has made it clear that Britain does not rule out any diplomatic option, provided British administration is resumed first. He has not closed the door to a UN or other kind of peacekeeping force, or to other arrangements by which Britain would make concessions on the issue of sovereignty.
So far both sides have been reluctant to share sovereignty and administration. The islanders themselves have rejected a ''lease-back'' deal on the model of Hong Kong, by which Argentina would take sovereignty but would immediately lease the islands back to Britain for a lengthy period.
One key question here was whether the islanders might have changed their minds. Mr. Pym has speculated that after the invasion, the islanders might want to remain British even more strongly.
A British man who has a half-share in a sheep farm on the islands said in London April 10 that the people were prepared to ''consider Argentine sovereignty in return for withdrawing the troops.'' The man, Edmund Carlisle, asked London to ''cool it.''
Fifteen civil servants on the island signed a letter to Mrs. Thatcher asking for people to be evacuated temporarily.
But the governor, Rex Hunt, now in London after being forced to leave, calls both views unrepresentative of island opinion.
Meanwhile, Lord Chalfont, former Foreign Office minister of state, believes that Britain should be ''realistic'' and not consider itself bound by the ''precarious basis'' of the islanders' opinions. Their best long-term interests, he says, may not be the same as their immediate short-term wishes.