Cabinet ministers were warned yesterday there was a "real risk"of the UK breaking up if the country crashes out of the EU with no deal, which could eventually lead to all four home nations choosing to go their own way.
In a frank meeting at Whitehall, Mrs May's top team were also told the UK Government should consider adopting a permanent "campaign mode" which could see millions of pounds committed to strengthening the Union in a bid to stave off the threat of a second referendum on Scottish independence.
David Lidington, the de facto deputy prime minister, reportedly warned those present that increasingly vocal calls north of the Border for an IndyRef2 posed a "significant and urgent political challenge" that would only increase if the SNP won an outright majority at the 2021 Holyrood elections.
A cabinet document shared with the Financial Times also revealed there are concerns at a Cabinet level regarding a rise in support for Plaid Cymru, the Welsh nationalist party.
Earlier this week, the First Minister of Wales hinted that his support for the nation’s place within the UK is not unconditional, suggesting that if Scotland was to break away from the Union then it would be right for Wales to “reassess” its position.
Mr Lidington told cabinet members that whoever replaces Mrs May as prime minister must not jeopardise the "integrity" of the UK.
One idea debated yesterday was a permanent "campaign mode" being adopted, which could see more spending on UK Government communications to make the case for the Union.
It was pointed out that while the Government's overall marketing budget is £440m, just £100,000 is spent on promoting the Union.
SNP leader Nicola Sturgeon said: "The fact that the UK government’s response to rising support for independence is to consider a rebranding exercise only shows how limited their understanding or genuine interest really is.