Branson's Virgin Trains, a joint venture between Virgin Group and Stagecoach (SGC.L), was outbid for the franchise to run services between London and north west England and Scotland earlier this month.
The tycoon attacked the decision as "insanity", saying FirstGroup's numbers do not stack up and called for an independent audit of the Department for Transport's (DfT) decision before the contract is signed on Tuesday.
"As far as the prime minister was concerned, there was a fair and robust process and the right decision has been made," Prime Minister David Cameron's spokeswoman told Reuters.
Rail and bus operator FirstGroup bid around 6 billion pounds to wrest the contract from Virgin, which has run the service for 15 years, for the next 13 years.
Branson has offered to run the service on a not-for-profit basis for a few months beyond the handover date on December 9 to allow time for a review.
However, the DfT said there would be no delay in handing the west coast rail franchise over to FirstGroup, despite Branson calling on the prime minister to back a last-minute review.
Branson is backed by more than 150,000 people, who have signed an e-petition urging the government to reconsider the franchise award.
However Tim O'Toole, FirstGroup's chief executive, said his company had "won the bid fair and square" and that he was confident the agreement would go ahead on time.
FirstGroup expects the route, which has annual revenue of around 900 million pounds, to generate sales growth of 10.4 percent and margins of roughly 5 percent over the life of the contract. (Reporting by Rhys Jones; Editing by Mark Potter)
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