But government says franchise deal will go ahead.
Sir Richard Branson offered to run the West Coast Mainline "for free" to give Parliament time to review the £10bn franchise's award to FirstGroup.
He said Virgin Trains and Stagecoach would run it on a not-for-profit basis after December - when they are due to hand over the franchise - if more time was needed for a review.
The West Coast Main Line route serves 31 million passengers travelling between London, the West Midlands, the North West, North Wales and the central belt of Scotland.
More than 150,000 people have signed an online petition against the decision.
But Transport Secretary Justine Greening said today: "We are going to get this signed off" Mrs Greening said the government would "push on" with the 13-year contract, which was a "good deal for taxpayers".
There has been pressure from Virgin Rail, which currently runs the line, and from the opposition Labour party, to delay the decision until Parliament returns.
The chairwoman of the Transport Select Committee has also called for a delay.
FirstGroup has said it would bring in key improvements for passengers, but critics fear it would not be able to afford the £5.5bn it was paying for the franchise and the government would have to take over the contract.
Mrs Greening told BBC Breakfast that all bidders had "bought into" the "fair and well-established process". She claimed that if Virgin had won the bid it would have "been perfectly happy with the process".
The Transport Secretary said the FirstGroup deal would provide more seats, more capacity and new services to places like Telford and Shrewsbury.
"If we want to move away from above-inflation fares, when it comes to franchising lucrative lines we've got to get a better deal for taxpayer, and that's what we've done," she said.
Aberdeen-based FirstGroup already operates a number of rail routes, including Great Western and ScotRail. The company, under the name First West Coast Limited, will take over the franchise from 9 December and is due to operate the service until 2026.
Virgin has run the franchise since 1997, during which time passenger numbers doubled.
Labour's Maria Eagle, the shadow transport secretary, has urged the government to put the contract on hold until MPs return from summer recess and have a chance to consider the deal. And Labour's Louise Ellman, who chairs the House of Commons transport committee, has written to Ms Greening asking her to delay signing the contract.
FirstGroup has said it would bring in key improvements for passengers. Introducing better wi-fi and food, more frequent trains and more seats, and would cut standard fares by 15%.
The firm said it would introduce 11 new 125mph six-car electric trains on the Birmingham-to-Glasgow route and provide more direct services between
However, the Virgin boss claimed promises made by FirstGroup in its successful bid were unrealistic and would lead to his rival's "almost certain bankruptcy".
In an opinion piece in the Daily Telegraph, Sir Richard described the government's decision as "outrageous, unjust and simply wrong".
His campaign to have the decision reviewed has been backed by businessman Lord Sugar, TV chef Jamie Oliver and the double Olympic gold medallist Mo Farah.
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