Senior government sources have told The Times of their concern that Nicola Sturgeon will use the start of the Brexit process to demand another vote on the future of the UK and that Whitehall is planning for that event.
The prime minister could reject the demand. However, such a move would risk causing a constitutional crisis.
Ministers have also been warned that, if Mrs May agreed, she would risk the break-up of the United Kingdom on a “coin toss”.
The UK government’s worries come after recent polls showed that support for Scottish independence was on the rise.
In a BMG poll published earlier this month, 49 per cent of those asked said they would vote yes in a second plebiscite.
Mrs May has also been told that she faces a double-headed “devolution crisis” next month, with Stormont elections on Friday unlikely to resolve Northern Ireland’s political crisis.
Concerns over Scotland and Northern Ireland were discussed last Tuesday by the cabinet, with senior figures saying that the impact of Brexit on the UK’s devolution settlement was the government’s greatest concern about the process of taking Britain out of the European Union.
The prime minister has rejected the SNP’s claim that Scotland’s rejection of Brexit requires it to be given a second chance to vote to leave the UK.
Writing in Holyrood magazine, she said: “In June last year, when the UK as a whole was asked if we should leave or remain in the European Union, every voter had an equal say and the collective answer was final.” She also said that there was “considerable common ground” between Westminster and Holyrood over the shape of the Brexit deal, adding that both wanted the “freest possible trade in goods and services between the UK and the EU’s member states”.
She also called on voters to use the local government elections in May “to send a clear message to the SNP that they do not want a second independence referendum”.
Responding to the Prime Minister’s magazine article, an SNP spokesman said: “There is already a cast-iron democratic mandate for an independence referendum - that was delivered in last year’s Holyrood election, however much the Tories might try to deny it.
“That mandate also stems from the EU referendum, which saw Scotland vote by a 24-point margin to stay in Europe - and Theresa May’s reckless pursuit of an economically ruinous hard Brexit will only strengthen opinion in Scotland against leaving Europe.
“The Prime Minister couldn’t be more wrong to suggest there is considerable common ground between her Government and the Scottish Government on Brexit - her party is hell-bent on taking us out of the world’s biggest single market, with all the economic damage that would cause, while we are intent on protecting Scotland’s vital national interests.”