More than 80 Conservative MPs face a major electoral challenge as a result of Theresa May’s pursuit of a hard Brexit, a major new study reveals.

In an analysis that exposes the scale of the party’s support from voters who backed Remain, it found that 3.5 million people in Britain voted to remain in the European Union in 2016 and then went on to back the Conservatives in last year’s election.

More than a million live in London and the south-east, with another 800,000 living in either the east of England or the south-west. It means there are significant areas of the country in which the party will have to hold on to Remain voters if they are to protect the seats from Labour or the Liberal Democrats.

The study, compiled using data from a 175,000-strong panel set up by pollsters YouGov, estimates that there are 86 Conservative-held constituencies where the number of Tory voters who backed Remain exceeds the party’s current majority.

Tories at risk include Amber Rudd in Hastings and Rye, Zac Goldsmith in Richmond Park, Paul Masterton in East Renfrewshire and Justine Greening in Putney.

The study makes clear that, while there has been much attention on voters in Labour heartlands who backed Brexit, the Tories also have an issue with voters who backed Remain. Recent evidence from the British Election Study suggests Conservative Remainers are more likely to care about Brexit than Labour Leavers.

In a sign of the crucial role to be played by Ruth Davidson, the Scottish Tory leader seen as a future national leader, the seats in question include 12 out of its 13 in Scotland. Davidson previously backed a softer Brexit than the one advocated by the prime minister. Last week, she also called for a Brexit that did not “raise the drawbridge and pull down the shutters”.

Other constituencies in which the Tory Remainer vote exceeds the party’s majority include six out of eight of its Welsh constituencies, more than half of the party’s 20 constituencies in north-west England and more than half of its 21 seats in London.

The study, by former Labour strategists Ian Warren and Kevin Cunningham of Election Data, also includes a worrying trend for the Tories in local byelections in areas with high levels of pro-Remain Conservatives.

In the east of England, south-east and south-west, the Conservatives have lost more than a third (68 out of 168) of the local byelections it was defending. More than half were lost to the Lib Dems, who are backing a referendum on the final Brexit deal.

It will give pause for thought to Tory MPs and the party’s high command as it attempts to form an electoral coalition able to deliver a majority. Senior Tories are openly pushing for a “sensible Brexit”, a compromise to soften the government’s position.

Former cabinet ministers Greening, Rudd and Damian Green went to No 10 last week in an attempt to persuade May to back a position that would unite most of the party around a compromise, which could see Britain stay inside a customs union with the EU for years after the transition period ends in 2021.

The new data will embolden Labour figures pushing the party into a much softer position on Brexit. While Labour has backed staying in a customs union with the EU, it has not backed remaining inside the single market or backing a new referendum on the final Brexit deal.

Eloise Todd, from the Best for Britain campaign, said: “This data shows that the Conservatives’ adoption of a hard Brexit could spell disaster for its election hopes, as well as the country.” The dozens of MPs at risk need to start representing their constituents and call on the prime minister to change course.”

The study also exposes a major potential role for voters who cast a ballot in the EU referendum, but opted not to vote in the last general election. There are 4.5 million of the voters, 2.9 million of whom backed Leave and 1.6m supported Remain. They could yet shape the next election should they be persuaded to cast a vote.