The Nationalists pounced on the blunder in a high-profile report from Vince Cable's business department, which will be published next week as part of the Coalition's case for the Union.
The report, the fourth in a series ahead of the referendum, claims Scots homes and businesses could suffer from a reduced postal service and inferior broadband coverage under independence.
Its key argument is that service and investment levels in Scotland, especially in rural areas, depend on large UK-wide programmes and cross-subsidies from profitable urban centres. It claims that the current six-day-a-week postal service and the uniform pricing of mail would be put at risk by a Yes vote next year. The EU standard for mail is a five-day-a-week service.
But it was the claim that Scots could have to pay international mobile-phone costs in England that prompted the fiercest row last night.
A briefing note circulated by Number 10 stated: "People from one country using their handset in the other could incur international roaming charges when travelling. Calls on both sides of the Border could inadvertently incur international roaming charges if their mobile phone connected to a mast on the other side of the border."
However, the European Commission is phasing out such charges for voice calls, texts and internet access, and has already cut them by 75% since 2007. Two weeks ago, commissioners voted to end the charges completely as soon as July 2014 to help create a single European telecoms market.
SNP MP Mike Weir said the roaming charges claim was a spectacular own goal by the Coalition.
He said: "Just this month the EU moved to abolish [charges] across Europe by next summer. It is complete incompetence and the Westminster government should have the good grace to cancel its publication and go back to the drawing board."
A Westminster source admitted the EU was reducing the charges, but insisted there was no certainty they would end on the timescale the Commission envisaged.
The report also warns that splitting integrated telephone and broadband services could see big changes for consumers, as companies used to the single UK-wide market would be reluctant to invest in rural areas, and may raise charges to cope with the new arrangement.
The Coalition government has allocated £530 million to roll out broadband coverage to rural areas, with Scotland getting £101m, or 19%, more than twice its population share of 8.5%.
The paper says that outside the UK, Scotland would no longer get that money, and any homegrown alternative would cost more because there would no longer be the same economies of scale to keep the price down.
Consumer minister Jo Swinson, the Liberal Democrat MP for East Dunbartonshire, said: "The UK's integrated infrastructure connects people and communities, creates jobs and supports trade. If Scotland left the UK, posting a letter or making a call could cost more."
A Scottish Government spokeswoman said postal services would be at least as good under independence as those operating currently.
"We would work to ensure that postal services continue in a similar way to the current UK-wide system, and the cross-border postal services between the Republic of Ireland and Northern Ireland. Both the Royal Mail and the Federation of Post Masters are clear there need be no disruption to services and that independence could offer real opportunities."