Writing on his blog on the Virgin website, Sir Richard said:
"From the moment we found out that FirstGroup had been made the preferred bidder with a completely unrealistic bid, we questioned the way the offers had been assessed, and asked the Government to review and explain how it came to its decision.
"We were convinced the process was flawed but despite our best efforts we were met with silence by the DfT.
"We also asked for the Government to appoint an independent adviser to look at the situation, which was turned down. Reluctantly we were forced to seek a judicial review."
He continued: "At the House of Commons Select Committee we called for all franchise competitions to be paused and a thorough, independent review of the process. We are grateful that Patrick McLoughlin is now doing this.
"We also appreciate the DfT publicly acknowledging these errors, and are hopeful they will now accept that Virgin Trains should carry on running the West Coast line and ensure that passengers continue receiving our team's award-winning service."
Boris Johnson says the rail franchise fiasco strengthens his case for taking charge of London's commuter services.
The future of rail services in the south-east has been thrown into disarray after ministers called a halt to several franchise competitions.