Ayr, Gordon and Stirling would all be lost to the SNP, according to a poll by marketing research company IQR.
The findings are part of a wider survey of 22,000 voters in the Conservatives’ 44 most marginal seats across the UK. The poll found three quarters of people are “dissatisfied” with the UK government’s handling of Brexit negotiations.
The poll shows the Ayr majority of six per cent would see a 19 per cent swing away from the Tories, meaning sitting MP Bill Grant would lose out.
And the flagship Gordon seat, which Colin Clark took from Alex Salmond last year, would also be lost with a 12 per cent shift wiping out the four per cent majority the party holds in the seat.
In Stirling, with a slim majority of just 0.3 per cent, Tory incumbent Stephen Kerr would also lose out with a swing of 18 per cent away from his party.
The survey of Tory marginals was commissioned by Global Britain, a pro-Brexit campaign group.
Brian Monteith, director of communications at Global Britain, said: “The clear message for any Conservative MP, whether in a Leave or Remain constituency, is ‘back Chequers and pay the price at the ballot box’.
“Chequers will not deliver Brexit, it will deliver Corbyn.”
The survey found 45 per cent of voters believe Brexit and the EU is the most important issue, compared to 17 per cent who believe the NHS is the most important and 7 per cent the economy.
Overall 73 per cent of voters were dissatisfied with the Government’s handling of Brexit negotiations.
The poll found 45 per cent of voters believed Chequers was bad for their family compared to 19 per cent who thought the plan was good.