A north-south high-speed rail line could cost £14 billion and have 186mph trains, according to Network Rail.
Trains on such a route - which has yet to get the go-ahead - would cover London to Glasgow or Edinburgh in two hours 35 minutes, said NR's deputy chief executive Iain Coucher.
The biggest demand would be a route "that swings up past Birmingham, Manchester and onwards to Edinburgh and Glasgow", Mr Coucher told a rail conference in London.
He added it was "difficult to see how a business case could be created" for including Leeds and Newcastle in the route, and going to Bristol and the south west of England and Wales "could not be justified".
In 2016, the annual number of passengers using the route could be 21.1 million, with this figure moving to 29.7 million by 2031.
The line should be capable of integrating with the London to Kent Channel Tunnel Rail Link and with existing rail lines for access to city centres. Services would run every 30 minutes.
Mr Coucher was presenting NR's views on the case for a high-speed rail line in a speech at the Institute of Civil Engineers in Westminster.
Such a north-south line has been the subject of debate for some years. It is expected that the line will form part of the report on transport which is being prepared for the Government by former BA chief executive Sir Rod Eddington.
The Government's views on the line are likely to be given in a rail White Paper next year.
Mr Coucher said the answer might not be a high-speed rail link if the question was one of dealing with capacity on the existing railway. There would have to be "a robust business case" for building the line, and it would have to rival the domestic airlines.
At speeds of 150-170mph, the London to Manchester journey would be one hour 15 minutes. Travelling up to 186mph would reduce journey times even further.
Annual revenue could be £ 750 million in 2016 and £1.1 billion by 2031, Mr Coucher said.
He said conventional high-speed technology should be used for the trains and that NR would not be keen to see innovative Maglev trains - deployed in China and which 'float' above the tracks - used on the line.
Mr Coucher said big questions had to be answered. "Can we resist the political pressure to include more stops along the journey, or the pressure to include other major cities - Leeds, Liverpool and Newcastle - where there appears to be no real economic business case?"
He said NR would want to be "a fundamental part" of any north-south high-speed project.
Commenting on Network Rail's vision for the line, shadow Transport Secretary Chris Grayling said: "The trouble is that like most of the Government's promises on transport this one is merely a vague promise for the future, without any money committed or a timetable set out.
"The public are right to be highly sceptical about these kinds of loose promises, which have no accompanying evidence to suggest they will come to fruition.
"Rather than concentrate on these vague aspirations, the Government should be concentrating on delivering projects that could actually make a difference to people's lives in the short term."