Sir Richard Branson yesterday offered to run the West Coast Main Line "for free" for a period of time, to enable MPs to scrutinise the successful bid from rivals, FirstGroup.

The entrepreneur's latest proposal, published after the Department for Transport (DfT) had insisted the new £10 billion franchise deal would be signed tomorrow, came as the online petition to retain Virgin as operator of the Glasgow-to-London route reached 125,000 names.

The offer was seized on by FirstGroup supporters as evidence of Sir Richard's desperation at losing a franchise so highly profitable for Virgin.

A source close to the Aberdeen-based company commented: "What it does show is how large his profit margins to be able to afford to make an offer like this. It points to the mistake he made when bidding, to not fully put in place a fair deal for taxpayers."

He added that delaying the handover of franchises due to take place on December 9 would have implications for a web of supplier contracts with the train operating companies, adding: "It is obviously not feasible and clearly a sign of an increasingly desperate man."

Sir Richard, in a proposal published on the internet yesterday, said FirstGroup's bid would lead to "almost certain bankruptcy". He said Virgin Trains and its partner, 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.

He wrote: "It is far better for MPs to have the chance to debate the issues, and question ministers on the detail before the decision is finalised.

"To assist in this process, there should be an independent audit of the DfT decision to ensure it has been based on correct criteria and reliable forecasting of customer numbers, revenue and payments to Government."

His plea came after Louise Ellman, the chairwoman of the House of Commons Transport Committee, wrote to Transport Secretary Justine Greening asking her to hold off signing the final contract because "important issues" had been raised. But the DfT said on Friday that its published processes and criteria "do not provide for a role in a live procurement exercise for the Transport Committee, which has not requested any kind of dialogue on this issue before now". It said Ms Greening was due to appear in front of the committee in early next month – after the deal has been ratified.

The online petition has been signed by 125,000 members of the public, in a campaign supported by double Olympic champion Mo Farah, businessman and Apprentice star Lord Sugar and celebrity chef Jamie Oliver.

But the source close to FirstGroup commented: "Richard Branson has got an awful lot of celebrity pals and has carefully mobilised a few of them. We can't compete on celebrity backers but we do know how to run railways."

Virgin has operated the West Coast Main Line since 1997 and has more than doubled annual passenger numbers over 15 years.

FirstGroup claims it will deliver better value for tax payers and plans major improvements including additional services, more seats, and lower standard fares.

However, analysts have warned that its bid is "very aggressive". Martin Griffiths, finance director of Stagecoach, told its shareholders in Perth on Friday: "Our bid had all those improvements too – that wasn't the reason we were rejected."