Prime Minister David Cameron must intervene in the row over the new West Coast Mainline contract to "get some sense" into the Department for Transport over the controversial deal, Sir Richard Branson has urged.

The Virgin boss has offered to effectively run the route for free to allow the decision awarding the 13-year franchise to FirstGroup to be re-examined.

It comes as Labour urged Transport Secretary Justine Greening not to sign off the contract until MPs have been able to scrutinise it in detail.

More than 100,000 members of the public have also signed an online petition against the decision, in a campaign supported by double Olympic champion Mo Farah, Apprentice star Lord Sugar and celebrity chef Jamie Oliver.

Sir Richard, who has claimed that FirstGroup's bid will lead to "almost certain bankruptcy", said Virgin Trains and Stagecoach would operate the joint venture on a not-for-profit basis or donate profits to charity if the franchise needed to be extended beyond December for a few months to allow Parliament to investigate the decision.

"I think that the person that can really intervene to try to get some sense into the Department for Transport is the Prime Minister and the Prime Minister is currently on holiday, the Chancellor is on holiday and we would like things delayed by a month or so," he told BBC Radio 4's Today programme."If, as a result of that, it means that the handover is delayed we would obviously be very happy to run it on a not-for-profit basis."

Labour said MPs had been denied the chance to raise concerns about the deal because it was announced during the Commons summer recess.

In a letter to the Transport Secretary, shadow transport secretary Maria Eagle wrote: "The decision appears almost exclusively a 'bottom line' one, driven by a particularly high pledge of payments to Government. You will know of the history of franchise contracts being brought to an early end, at least in part because of over-ambitious payment promises that proved impossible to realise. There are fears that lessons have not been learnt."

FirstGroup claims it will deliver better value for taxpayers. It plans major improvements to the InterCity West Coast franchise to enhance the customer experience, including improved wifi and catering, as well as additional services and more seats and reducing standard anytime fares by 15% on average.

Bob Crow, leader of the RMT transport union, said: "The shambolic handling of the West Coast franchise has not only left 800 of our members' jobs hanging by a thread but has also exposed the chaos right at the heart of the Transport Department and the insanity of government rail policy which revolves around a poisonous cocktail of cuts, fare increases and private profits. The only sensible solution is renationalisation if we are to avoid the anarchy of an action replay of the east coast route collapse."

The Press Association, photo by The PM office