"I didn't want to be away for another night," he smiled. So he chartered a plane to fly to the islands, found a blackboard and chalk and wrote on it, "Virgin Airways, $39 a ticket." He filled the plane, and made it to the islands that night.
The next day he called Boeing's head of sales, and said he wanted to buy a second-hand 747. After months of discussions he did so, and set about selling seats to fund its purchase.
"One thing; the name doesn't work," said the Boeing sales chief. "With a name like Virgin, passengers will think it won't go all the way."
More than three decades on, he has more than proved the salesman wrong. But, after warning last week that it will return to a loss this year, the airline is suddenly facing some strong headwinds.
Craig Kreeger, the US-born airline executive who was drafted in to run Virgin Atlantic four years ago, is remarkably frank.
"2016 was a very good year in difficult circumstances," he says. "It was our third year in a row of profitability... but our expectation for 2017 is to be loss-making."
The timing of his remarks, as the airline sets out expansion into Seattle as well as new flights from Manchester to San Francisco and Boston, may seem odd. But it would appear to be all about under-promising and over-delivering. If he delivers a profit he will be seen to have done a good job. If not, he said it wouldn't.
The airline's latest woes are three-fold; the result of sterling's recent weakness, a sharp spike in the price of fuel and an increase in competition.
By far the most significant of those is its new currency problem.
Kreeger estimates the fall in the pound cost Virgin £50m in profit in 2016. Fewer Brits are willing to travel across the Atlantic, while costs such as fuel and new planes are billed in dollars. The fact that this has come at the same time as Virgin has repositioned back to the US, thanks to its joint venture with Delta - which took a 49 per cent stake in the business in 2012 - could be seen as slightly problematic by some.
Gone are routes including Mumbai, Tokyo and Sydney, while Atlanta and Seattle have been added.
Branson's chief lieutenant is more optimistic, however. "Having a strong US partner means that it's pretty easy to turn on the taps and move more Americans in this direction," Kreeger explains.
It is a plan which may work. Gerald Khoo, aviation analyst at Liberum, acknowledges that Virgin has "enormous brand presence in both the UK and the US".
"Virgin Atlantic has survived worse, and now has the financial backing of Delta," he surmises.
Kreeger describes the US expansion as "step one" in his fight-back plan.
"The same thing is true of our sales efforts in China, Hong Kong and South Africa. We're spending more of our resources to drive traffic into the UK.
"The other thing we can do is keep trying ways to become a more efficient business."
Fuel is also causing problems. The price of jet fuel has risen by 50 per cent in less than 12 months.
"The good news is that all of the hedges we had prior to 2015 have unwound," Kreeger explains.
That means costs should now be more reflective of lower prices.
"All the hedges now are in the new world," he continued, but refused to reveal further details.
The third threat, and one which could have a slightly more lasting effect than the others, is changing competition.
Although in the past the airline has thrived on its rivalries - its spats with British Airways in the early days are the stuff of legend - it is now having to cope with low-cost carriers across the Atlantic.
Norwegian is perhaps the strongest of these. Offering no-frills flights for budget prices, it is attractive for leisure travellers looking to make their money go further in the US. A quick comparison shows that flying out in October, Norwegian is charging £353.70 for a return economy flight to San Fransciso from Gatwick, compared with Virgin's £551.57 for the same return on the same dates from Heathrow.
But it's not just Norwegian that is a threat. Canada's Westjet is offering flights to Toronto from £192 (Virgin doesn't fly direct to Toronto but does offer connecting flights through Delta), while Icelandair is upping its game in the UK market, offering flights to the US, albeit via Reykjavik, for competitive prices.
And that's all before Level - the new airline set up by British Airways and Aer Lingus owner IAG - starts flying from London.
Kreeger believes that Virgin is up to the challenge.
"We managed to increase our load factor last year despite an equally large capacity increase in 2016. So we don't have to match them pound for pound but we have to get close enough that we give customers a good reason to choose Virgin Atlantic because of what they get on our planes.
"We think that strategy will work in this space."
He refuses to be drawn into criticising Level, saying only "that's a Spanish low-cost carrier that will probably connect with their Vueling operation".
Instead the Virgin modus operandi, for now at least, is not to go down a similar route and create an airline within an airline, but to focus on its existing operation, which Kreeger says is "uniquely Virgin".
"It's our job to make sure customers know whose metal they're flying on. We can meet expectations regardless."
Branson agrees, adding: "We must compete with anybody on low prices as well as quality.
"That's what Virgin Atlantic has done for 33 years and will continue to do for the next 33 years; but we'll do it in away that doesn't bastardise our product."
Not everyone is quite so convinced.
"No airline can survive unless it is prepared to adapt and change and I fear that Virgin is in danger of falling into a rut," explains Howard Wheeldon, the independent industry analyst.
Liberum's Khoo is also bearish on what these new challenges could mean. "Norwegian is certainly a bigger threat in the low-frequency leisure market than the business traveller market," he says, putting it head-to-head more with Virgin that British Airways. "Passengers' expectations of service from Virgin are high," he adds, explaining that if it has to adapt to lower its offering to compete with Norwegian on cost, there could be problems.
Wheeldon suggests that one solution to that may be to move more upmarket, and reduce its exposure to the leisure market, but that then could lead to whole cabins flying empty, something which no airline can afford to allow, or a drastic reordering of some of its planes to focus on its popular Upper Class and Premium economy offerings.
Virgin's secret weapon in the fight against Norwegian and others is Virgin Holidays. Approximately 50 per cent of the holiday firm's customers fly with Virgin Atlantic. The holidays arm had a good year in 2016, delivering £19.1m of pre-exceptional pre-tax profit, up 75pc on 2015.
Despite its successes, the reality is that Virgin is entering somewhat uncharted territory as it attempts to respond to new business models while retaining its brand value.
Still, 2017 will not all be bad news. In December 2012, Willie Walsh, chief executive of BA-owner IAG, wagered that Virgin would not be independent in five years time, and instead would have been swallowed up by Delta. The loser gets a knee in the groin from the winners. With just nine months to go until that deadline, the billionaire grins when it's mentioned.
"I'm looking forward to calling it in," Branson smiles.
Whether he'll be able to say the same five years from now depends on how the airline he created in unique circumstances 33 years ago responds to challenges firmly on its horizon.
