But Virgin, which earlier this week unveiled its new Pendolino tilting trains to the world's media, is adamant that Railtrack must deliver the project as originally planned.
The BBC's Midlands transport correspondent, Peter Plisner, reports on why Virgin's high-tech plans may be running into trouble.
Sir Richard Branson's high speed tilting trains may not be able to run at their top speed of 140mph.
The cost of upgrading the track they are to run on has risen dramatically and Railtrack wants to make changes.
It could mean the shorter journey times that were promised might not be achievable.
But the cost of the project is continuing to rise.
Originally estimated at just over £2bn, it is now sitting at about £6bn.
Railtrack 'must deliver'
Railtrack, which is managing the project, has confirmed that it is in talks with Virgin, with which it has a contract, about train speeds in some areas.
Tony Fletcher, the project's general manager, said "The issue that's up for discussion is the extent of the 140mph running.
"The journey times may be tweaked, but the capacity (of the new line) will be held."
But Virgin, which earlier this week unveiled its new Pendolino tilting trains to the world's media, is adamant that Railtrack must deliver the project as originally planned.
Chris Green, chief executive of Virgin, said: "Railtrack would be in serious breach of a contract they have signed and we'd be talking very big money.
"We don't want that, we want a railway that works at 140mph.
"Our starting point is that we have a contract which took two years to negotiate, both parties signed it, let's make it work."
Massive disruption
Negotiations are also taking place about how and when some of the work will be carried out.
Railtrack wants to close some parts of the West Coast route, something which could cause massive disruption to passengers.
But Virgin and other train operators are opposed to the idea.
The West Coast Main Line runs from London to Scotland and is one of the busiest railways in Europe.
It was last upgraded in the 1960's, when the line was electrified.
However, some of the infrastructure still dates back to Victorian times and the line now badly needs to be modernised.