Mr Green, 55, faces an uphill task. Virgin owns two of the most elderly and problematic rail franchises. The West Coast line from London to Glasgow has had little work done on it since it was electrified in the Sixties. CrossCountry runs trains that connect all corners of the UK and cover distances of up to 800 miles, making them liable to delays.
Last year the franchises attracted more passenger complaints than any other operator and the latest performance figures showed the flagship London-to-Glasgow service had the worst punctuality record in the country, with almost 20 per cent of trains running late. The letters columns of the national papers are full of horror stories from passengers. Virgin is a butt of the nation's jokes to an extent that only British Rail could rival.
The business probably reached its nadir at the Labour Party's annual conference when Virgin failed to deliver party delegates to Blackpool. Richard Branson went on the radio to tell shocked listeners: "We fucked up, we fucked up badly."
The appointment of Mr Green is a sign that Mr Branson is desperate to restore the reputation of the train business, whose performance threatens to undermine the Virgin brand. Mr Green has been hired on a five-year contract with a two-fold mission - to deliver a markedly improved service on the existing network and ensure the pounds 1.8bn worth of new trains will be delivered on time. He should be qualified for both, as one insider praised his "exceptional" marketing ability and his track record on train procurement.
The first task looks the more challenging. Mr Green said he would launch a "back-to-basics" strategy to improve punctuality. He has embarked on a 100-day mission to get views from staff and passengers about the way forward. "I want added professionalism in everything we do. Whatever we do, let's do it well and let's get rid of those silly little mistakes that have annoyed customers. Running out of tea is just unforgivable," he said. "People have taken their eye off the ball while making large train orders or contracting out work to third parties. We have to get back to basics.
"It will be a process of continuous improvement for the next few months. It is about getting the boring details right. I would hope to be able to show an improvement every three months."
Virgin recently provoked an outcry by increasing first-class fares to Manchester by 10 per cent and to Birmingham by 19 per cent while offering better deals on tickets booked three days in advance.
Mr Green said Virgin's prices had been lower than other operators, but added: "I would not expect us to have higher prices." He had "four or five" new initiatives up his sleeve but said it was too early to go into details as he only officially took over the reins from Brian Barrett, who is retiring, on Monday.
Despite Virgin's poor reputation, he said that only 30 per cent of delays were caused by Virgin, with the rest down to other operators, Railtrack or acts of God. Under the deal for the new trains, the train builder Alstom would take responsibility for the existing fleet under a contract that demanded a 33 per cent cut in delays due to train faults. He insisted he wanted to build a new relationship with Railtrack, which is spending pounds 1.2bn on the West Coast line, following recent arguments over who was to blame for falling standards. "Throwing rocks at each other may feel good but it won't solve a single problem."
The two new fleets of trains are the key to the long-term success of the Virgin rail business, which is now 49 per cent owned by Stagecoach. About pounds 1.2bn is being spent on a fleet of 53 140mph tilting trains for the West Coast line which will achieve the "holy grail" of Glasgow in under four hours, said a spokesman. The rest is being spent on 78 diesel trains for the CrossCountry route.
Mr Green has been here before. From 1992 to 1994 he was managing director of InterCity, the profitable high-speed train business of BR that includes both CrossCountry and West Coast. Ironically, the man in charge of the West Coast line at the time was Ivor Warburton, who resigned last week as director of business development. Mr Green said the pair remained friends.
His successes in turning around the fortunes of ScotRail and the creation of the Network SouthEast business led to him being hailed as the best chairman BR never had. He quit in protest at the plans to break up the network at privatisation. His departure in 1995 for the top job at English Heritage took the industry by surprise.
Observers say Mr Green's career with BR made him the right man for the top job at Virgin Rail. One said: "He has an impressive track record. He is probably responsible for the procurement of more new trains during this period than any time since. His no-nonsense attitude and exceptional marketing ability is widely believed to be a long-needed counter to some of the more disastrous promotions dreamed up by Virgin's novice marketing people."
Mr Green declined to reveal his pay package but he said he had been given a "fair deal" by Mr Branson. He said he would have been interested in the job of chairman of the Strategic Rail Authority, the new body being set up by the Deputy Prime Minister, John Prescott, to regulate the railways.
However, it is unlikely he would have been accepted for the post following a Commons Public Accounts Committee report last year that said he was unfit to hold public office. This followed his high-profile departure from English Heritage amid accusations of inaccurate expenses claims. However, there was no suggestion of any fraud.