Almost half of Labour supporters and an even higher proportion of Greens say they are ready to switch to the Liberal Democrats if it would help defeat the party committed to Brexit in their constituency.
More than a third of Lib Dem backers would make the opposite journey at the ballot box – potentially delivering 60 seats and a mortal blow to Mr Johnson’s hopes of winning a majority.
The poll, for the People’s Vote campaign, comes after it unveiled plans for the biggest vote-swapping drive in history, to support the best-placed candidate in more than 100 battleground seats.
“Tactical voting could damage Johnson’s prospects fatally, meaning Labour could make net gains from the Tories,” said pollster Peter Kellner, the former YouGov president.
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Anti-Brexit voters in the key 100-plus seats are being promised clear, independent advice on which candidate to back, in order to maximise the chances of electing a pro-EU MP.
In its first 20 endorsements, People’s Vote recommended they back the Lib Dem candidate in nine seats and the Labour candidate in the other 11 seats.
Now, in the YouGov poll, 35 per cent of Lib Dem and 42 per cent of Green voters are ready to switch to Jeremy Corbyn‘s party if they “thought that the only parties with a realistic chance of winning in your constituency were the Conservatives or Labour”.
In Conservative-Lib Dem contests, half of Labour supporters and a similar share of Green supporters said they would lend support to the Lib Dems, with hardly any voting Conservative.
Mr Kellner added: “These figures suggest that tactical voting on this scale could cost the Conservatives up to 60 seats.
“Labour would be the beneficiaries in around 50 and the Lib Dems up to 10.”
Even without tactical voting, the prime minister is on course to fall short of his dream of a majority that could give him greater freedom to purse the Brexit outcome he wants, the poll of more than 2,000 voters found.
It put the Conservatives on just 30 per cent, but ahead of Labour (23 per cent), the Liberal Democrats (22 per cent) and the Brexit Party (14 per cent).
On a uniform swing, this would leave Mr Johnson 19 seats short of control of the Commons, with both Labour and Conservatives losing seats to the Liberal Democrats and the SNP.
An election remains on the back-burner, after the opposition parties twice joined forces to prevent the prime minister calling one until he has secured a delay to prevent a no-deal Brexit on 31 October.
With Mr Johnson still refusing to seek that extension to Article 50, it means no election until the end of November at the earliest when – if the UK is still in the EU – he will be a weakened figure, his opponents believe.