Coming just days after Mr Branson was photographed with the Princess of Wales naming a new Virgin Atlantic airbus, there is seemingly no end to the tycoon's public relations triumphs.
But how does he do it? Is he a brilliant self-publicist? Is it just luck? Or is it simply that nothing succeeds like success?
A mixture of all three appears to be the answer. As far as the released Britons are concerned, Sir Edward rang Mr Branson early on Monday morning and asked him whether he could supply a jet for the private rescue mission.
Mr Branson, sitting in the upper-class lounge at Heathrow waiting for the Princess to arrive to name his new jet, said yes immediately and was briefed on the details of the trip later.
In October 1990, Mr Branson, at Sir Edward's request, arranged for a jet to fly 40 sick and injured hostages out of Iraq, and in September that year King Hussein of Jordan asked Mr Branson, whom he knows, to fly in relief supplies for 300,000 Kuwaiti refugees.
Sometimes, then, Mr Branson simply lends a hand when asked for help. Other events are more premeditated. The request to the Palace for the Princess to name the new jet, for example, was made in July. Hot-air ballooning trips across the Atlantic and Pacific oceans were adventures designed to promote Virgin Atlantic. As was racing across the Atlantic in a high-speed power boat in 1986. Mr Branson does not rely on a phalanx of public relations advisers. There is one press officer in each of the Virgin companies and Will Whitehorn, corporate affairs director, and his assistant in Mr Branson's private office.
Mr Whitehorn, who has been with Virgin for six years, says that before 1984 Mr Branson rarely gave press interviews, but that in that year Sir Freddie Laker advised him to achieve a high business profile in order to compete with the big airlines.
'Shout long and hard at the first sign of trouble,' Sir Freddie said. Advice that was to prove invaluable during the British Airways 'dirty tricks' campaign when Virgin Atlantic had to defend itself from a stream of untrue allegations.
Max Clifford, the astute master of public relations, says that while Mr Branson is a natural showman, Britain also delights in his swashbuckling image of self- made English entrepreneur.
'He's a man for all occasions,' Mr Clifford says. 'He knows a good opportunity and enjoys it but there are a lot of people out there who he has helped at the same time. There are lots of people who benefit from Richard Branson, other than Richard Branson.'
Mind you, Mr Clifford adds, Mr Branson ought to be careful that he does not go over the top. Putting an arm around the Princess of Wales was perhaps a bridge too far.
British Airways was putting a brave face on Virgin Atlantic's latest PR triumph. It was delighted the Britons had been released. BA would also 'have been happy to fly them back to the UK'. It just wasn't asked.