The Chinese authorities had ordered the flight to land on Tuesday morning after it violated restricted air space, but the balloon's crew refused to put down because they said it was too dangerous.

Mike Kendrick: Richard said: "brilliant, brilliant, brilliant!"

Project Manager Mike Kendrick said the crew were delighted with Beijing's change of heart. "Perhaps now they can start to enjoy this flight. We are so pleased.

"It was a showstopper. I have spoken to Richard and he is absolutely delighted. 'Brilliant, brilliant, brilliant,' is what he said.

"If we weren't so busy and our jobs weren't so important, we'd get drunk."

Branson: Delighted with the go-ahead

China's U-turn came after two days of frenetic diplomatic activity involving Prime Minister Tony Blair, former Prime Minister Ted Heath, British Embassy staff and US officials.

Looking ahead, Mr Kendrick said that the crew were attempting to manoeuvre the balloon into the tail end of the Pacific Jet - a body of air that will hopefully carry the flight over the Pacific Ocean at speeds of up to 200mph.

The BBC's Lisa Holland: Record attempt is back on course

He said the team was taking the round-the-world attempt "one leg at a time" and judged its chances of success were now "50-50".

"We've just got to find the fastest and most direct route out of China," he said.

BBC Correspondent Daniela Relph reports from the project control centre

At a press conference earlier on Tuesday, he said the balloon was in danger of icing up and the crew were having difficulty steering it. They have also used more fuel than they had expected to by this stage.

The capsule's satellite telephone antennae have already iced which is making communication difficult, although the crew can still be reached by email.

The BBC's Carrie Gracie: "No accidental shooting down of the balloon"

Piloted by Branson, American Steve Fossett and Sweden's Per Linstrand, the balloon crossed from Nepal into Chinese-ruled Tibet just before 2200 GMT on Monday.

It was off course as it crossed the Himalayas due to diversions the crew made around violent Mediterranean storms and air strikes in Iraq.

The result was that it entered China north of an approved "air corridor" and is currently over the mountainous Tibetan plateau - some of the coldest and most inhospitable terrain in the world - about 10 miles inside China.

Personal record

At an earlier press conference on Tuesday afternoon, Mr Kendrick said the idea of the balloon coming down in its present position was "horrific".

Branson and Lindstrand have already broken their personal duration record of 48 hours set during their 1991 crossing of the Pacific in a hot air balloon.

If the flight continues on its present course, it will fly over San Francisco on Christmas Day and complete the round-the-world journey over the UK on New Year's Eve or New Year's Day.