LONDON -- Bermuda will have to rely on itself, not the British Government, to soften the impact of a US military withdrawal from the Island.

That is the over-riding impression after Premier the Hon. Sir John Swan's two-day visit to London ended yesterday with talks with Foreign Secretary Mr.

Douglas Hurd.

Despite a pledge from Prime Minister John Major that his Government would do what it could to prevent or delay any US withdrawal, indications at official levels were that Bermuda had to carry the ball on preventing the abrupt closure of the US Naval Air Station.

The point did not seem to be lost on Sir John.

"External affairs will be vital to Bermuda,'' he said after meeting Mr. Hurd at the Foreign and Commonwealth Office. "And it will be up to us.'' Prime Minister Major said as much to Premier Swan at the end of their meeting at 10 Downing Street on Wednesday.

"What you're doing is the best approach and vital to the process,'' he said of Sir John's diplomatic efforts in London and Washington.

Later, Mr. Mark Lennox-Boyd, the Under-Secretary of State with responsibility for Bermuda, said at a luncheon in honour of the Premier that his Government's approach to Bermuda was to "let you run things.'' That hands-off position was reflected in another way by Foreign Office officials who saw the Premier's visit as an opportunity to "get reacquainted'' -- a rather laid-back depiction that did not match the Premier's sense of mission.

In addition to the hands-off approach that puts the diplomatic onus on Bermuda, a series of significant foreign issues are pressing Mr. Major's Government.

With Britain preoccupied with Europe and the US determined to focus on the home front, the Premier said there is a risk developing of Bermuda becoming as isolated politically as it is geographically.

Although the UK Government said it would help Bermuda dissuade the Americans from closing the base abruptly, Sir John wondered how far it could take that commitment.

"Their agenda is focused on big things,'' he said. "And they are being bombarded with other issues. The bottom line is that the initiative rests with us. This issue will be up to us.'' Another concern for the Premier, and one that hints Bermuda is virtually alone in its concerns, is the momentum of historic change. It is an era, he said, when historic relations and assumptions are weakening rapidly. The world is changing, he said, and Bermuda must be up to speed to cope with it.

Just what is at stake for Bermuda in the event of a base closure trickled out in the past couple of days.

It currently costs the US Government between $18 million and $25 million to run Base operations that include the Civil Air Terminal.

The cost Bermuda would have to assume in the event of a US pull-out is roughly equal to the revenue Government lost in the midst of recession last year -- now accepted as the most wrenching economic performance since the depression.

Sir John yesterday acknowledged that taking on the airport operation would mean a massive re-ordering of Government spending and a reduction in services to the public.

The changeover would also require an enormous national commitment to get the airport's 24-hour a day operations up to acceptable international standards.