London — If a British invasion of the Falkland Islands does succeed, a new set of disturbing questions opens up, centered on one basic issue: What next?
Britain may have to hold on to the islands against Argentine air and perhaps naval attacks for many months, maybe even for years, if Buenos Aires refuses to negotiate.
How long can Britain maintain a garrison there, 8,000 miles from home base? ''It might have to be years,'' says Robert Elliot, an analyst with the International Institute of Strategic Studies here. ''Military action is never really a solution. Only diplomacy is.''
Britain hopes that Argentina would be forced to negotiate for settlement, perhaps after the military junta is forced from office for failing to hold the Falklands, and civilian government is restored.
Neither development can be predicted with certainty, however, and there are more questions to be asked:
How costly would a British invasion be? How long will British public opinion, and the House of Commons, be prepared to keep British forces on the Falklands if those costs are high?
At this writing, British officials were indicating that if they do regain the Falklands, their negotiating stance will be tougher. Argentina, sources say, has been given every chance to obey Security Council Resolution 502, which calls for a cease-fire, withdrawal of Argentine troops, and talks on differences. Britain has yielded ground on a number of negotiating demands.
''The prime minister feels she has been too accommodating and has been hanging on too long,'' a source close to her said privately May 19.
Mrs. Thatcher herself confirmed on the same day that she was considering whether a United Nations presence on the island after Argentine forces had been withdrawn might be preferable to returning to direct British administration in the person of Rex Hunt, ousted as islands governor when Argentina seized the Falklands.
Earlier, London had insisted on restoring British administration.
Mrs. Thatcher has also dropped her demand that the wishes of the islanders must be ''paramount.'' Now she indicates only that they must be considered.
Until now she has also indicated she was prepared to pull back her task force in stages, provided Argentina was ready to withdraw.
But if she seizes the Falklands by force, the conflict will move to a new phase.
She will take Argentine forces prisoner, and because the two countries are not formally at war, she will also send them home.
She is then likely to demand that US troops be among any interim UN force, and that the interim period be longer than Argentina has been ready to accept.
The danger in this is that it may simply stiffen Argentine resolve and lead to a state of seige. Argentine air forces would try to bomb the British off the island.
Britain would have to maintain a large garrison there indefinitely, and defend it, at escalating costs to its own economy.
As this article was written, Britain was preparing to attack Argentine positions with forces heavily outnumbered in the air and on the ground.
Military observers felt that Britain had a good chance of success, given its professional troops and good training. But, as Robert Elliot pointed out, any invasion could be ''pricey.''
Earlier plans to increase political pressure by occupying areas of West Falkland Island seemed less likely. Prime Minister Thatcher was thoroughly fed up with what she saw as Argentina's attempt to spin out negotiations at the UN while the British task force tossed on the high seas of the wintry South Atlantic.
More likely, it was felt, was a British attack on the Port Darwin and Goose Green areas of the East Falkland Island, or an occupation of the northern part of the same island.
But most probable, it was said, was an attack on the 10,000 or so troops in the Port Stanley area itself.
British troops on the task force numbered about 4,000 -- fewer than half the defenders. Normal rules of war say an attacker needs a 3-to-1 advantage. In other words, Britain ought to have 30,000 men instead of 4,000.
With the arrival of reinforcements, Britain now has 37 Harrier jump-jets to put against about 100 Argentine Super Etendard, Mirages, Daggers, Canberras, and Skyhawks.
The Argentine Air Force has been notably restrained, apart from sinking the destroyer Sheffield. Air Force Chief Brig. Gen. Basilio Lami Dozo has reportedly been more dovish than the two other junta members.
But on May 18, he threatened a ''massive attack'' on the British fleet, and he may well have felt he had to step up his attacks or be accused of sabotaging hopes for victory. If Argentine aircraft do try to bombard British forces, London would have to consider whether to bomb Argentine airstrips on the mainland.
At this writing, officials were saying privately they expected that hostilities could be contained within the war zone itself.
Constant bombardment of British invasion forces might change the picture. A source close to Mrs. Thatcher said May 19 that a formal declaration of war would be needed before any attacks on the mainland could be launched.
Another disturbing element: the potential of Argentina's two small, 1,800-ton T-209 submarines to sink British ships. Nothing has been heard of them for weeks , but they could be tucked into inlets close to Port Stanley, and their wire-guided missiles are more than enough to sink the aircraft carrier Hermes or the assault ship Invincible.