Sir Richard Branson and fellow leading businessmen will warn ministers this week that the world is running out of oil and faces an oil crunch within five years.

The founder of the Virgin group, whose rail, airline and travel companies are sensitive to energy prices, will say that the ­coming crisis could be even more serious than the credit crunch.

"The next five years will see us face another crunch – the oil crunch. This time, we do have the chance to prepare. The challenge is to use that time well," Branson will say.

"Our message to government and businesses is clear: act," he says in a foreword to a new report on the crisis. "Don't let the oil crunch catch us out in the way that the credit crunch did."

Other British executives who will support the warning include Ian Marchant, chief executive of Scottish and Southern Energy group, and Brian Souter, chief executive of transport operator Stagecoach.

Their call for urgent government action comes amid a wider debate on the issue and follows allegations by insiders at the International Energy Agency that the organisation had deliberately underplayed the threat of so-called "peak oil" to avoid panic on the stock markets.

Ministers have until now refused to take predictions of oil droughts seriously, preferring to side with oil companies such as BP and ExxonMobil and crude producers such as the Saudis, who insist there is nothing to worry about.

But there are signs this is about to change, according to Jeremy Leggett, founder of the Solarcentury renewable power company and a member of a peak oil taskforce within the business community. "[We are] in regular contact with government; we have reason to believe their risk thinking on peak oil may be evolving away from BP et al's and we await the results of further consultations with keen interest."

The issue came up at the recent World Economic Forum in Davos where Thierry Desmarest, chief executive of the Total oil company in France, also broke ranks. The world could struggle to produce more than 95m barrels of oil a day in future, he said – 10% above present levels. "The problem of peak oil remains."

Chris Skrebowski, an independent oil consultant who prepared parts of the peak oil report for Branson and others, said that only recession is holding back a crisis: "The next major supply constraint, along with spiking oil prices, will not occur until recession-hit demand grows to the point that it removes the current excess oil stocks and the large spare capacity held by Opec. However, once these are removed, possibly as early as 2012-13 and no later than 2014-15, oil prices are likely to spike, imperilling economic growth and causing economic dislocation."

Skrebowski believes that Britain is particularly vulnerable because it has gone from being a net exporter of oil, gas and coal to being an importer, and is becoming increasingly exposed to competition for supplies.

"This is likely to put pressure on the UK balance of payments and in a world of floating exchange rates is also likely to put downward pressure on the valuation of sterling. In other words, the positive benefits to the valuation of the pound as a petrocurrency are now eroding," he said.

The question of peak oil came to centre stage last November when a whistleblower told the Guardian the figures provided by the IEA – and used by the UK and US governments for much of their planning scenarios – were inaccurate.

"The IEA in 2005 was predicting that oil supplies could rise as high as 120m barrels a day by 2030, although it was forced to reduce this gradually to 116m and then 105m last year," said the IEA source. "The 120m figure always was nonsense but even today's number is much higher than can be justified and the IEA knows this."

But Saudi Arabia launched a counter-strike at Davos, insisting the issue was overblown. "The concern about peak oil is behind us," said Khalid al-Falih, chief executive of Saudi Aramco.

Tony Hayward, the BP chief executive, downplayed fears about dwindling supplies in an interview with the Guardian last week.