Expensive plans to speed rail commuters from London to Glasgow and Edinburgh in under three hours would be scrapped if Scotland votes for independence, a cabinet minister has warned. The Department for Transport agency overseeing High Speed Two is currently examining options for a third phase of the much criticised railway, which would pour billions more on to a budget that has already topped £40bn.

There would probably be a link from Manchester or Leeds – the two cities where the "Y"-shaped second phase ends – to Scotland. This would ultimately shave well over an hour off journeys between the capital and Edinburgh or Glasgow.

However, a cabinet minister told The Independent on Sunday that an extra link was almost inconceivable in the event of a Yes vote for independence in September, due to the added cost burden on UK finances to a country that was no longer in the union.

Download the new Independent Premium app Sharing the full story, not just the headlines

The source said: "The high-speed railway is a substantial public investment and it's difficult to see how that investment would be justified from south of the border."

A Scottish pro-union MP added: "Many of us would like to see HS2 extended to the central belt of Scotland, but I couldn't see an independent Scotland being able to afford it nor English taxpayers subsidising them."

An SNP spokesman for Scotland's Transport minister, Keith Brown, hit back: "This is exactly the kind of high-handed, arrogant, patronising attitude from Westminster that is driving so many people across Scotland to the Yes campaign and towards a Yes vote in September."

Under current plans to the end of Phase Two, it would take three hours, 38 minutes to travel between Edinburgh and London against four hours, 23 minutes today. Glasgow to London would be half-an-hour faster, while Birmingham residents could reach Edinburgh in three hours 14 minutes against a little over four hours now.

The second phase alone is expected to boost Scotland's economy by £3bn a year, but the Government and Sir David Higgins, who leads HS2 Ltd, are keen to expand the new railway further and make it the spine of Britain's network. In November, Transport minister Baroness Kramer asked HS2 Ltd to look into options for a third phase taking the line into Scotland, with findings due this year.

As well as the option of extending HS2, existing lines could be upgraded, or there might be a combination of the two. There has also been talk of a distinct line requiring an interchange, crossing a city via metro links, in a move that would effectively create a High Speed Three.

There is a well-organised campaign against building any of HS2, which will start with a link between London and Birmingham, due to the hefty price tag and suggestions it would ruin great swathes of the English countryside. However, Scottish business groups are hopeful that HS2, or at least a variant of it, will ultimately reach their major cities.