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Pro-Remain group Best for Britain has published an estimate saying the actions of less than 1% of voters from 2017 could swing the result away from the Tory leader.
The MRP poll – a type of poll that can produce more accurate results than normal ones - shows the Conservatives winning 366 seats, which would give Mr Johnson a majority in the House of Commons.
But Best for Britain has found that many of the seats the party is expected to win or hold are vulnerable, and identified 57 target seats where pro-EU voters could prevent a Tory win.
“Nationally, Best for Britain estimates it could take as little as 117,314 pro-EU voters using their vote tactically to prevent a Tory majority – representing less than 1% of those who voted in 2017,” the group said.
Of the 57 target seats identified, 27 would need fewer than 2,000 tactical votes to stop a Conservative majority, the group claims.
The rest would only need up to 4,000 Remainers to vote tactically in the general election and if they did so, Best for Britain thinks the Tories would end up on 309 seats.
That would leave Mr Johnson struggling to pass his Brexit deal – which Best for Britain has encouraged with a tactical voting website.
He called an election to break the Brexit deadlock and pass the deal his government agreed with the EU.
The data was based on 39,476 respondents.
Best for Britain CEO Naomi Smith said: “Our data shows that tactical voting will be decisive at the upcoming election.
“Even with the Brexit Party collapse, there are still lots of seats in play for Remainers.
“This is crucial as it means they could be won by pro-EU parties if voters hold their nose and vote for the party with the best shot of beating the Tories.”
Following concerns the Brexit Party could split the Leave vote, leader Nigel Farage announced earlier this month that the party would not stand against the seats the Tories won in 2017.
The Lib Dems, Plaid Cymru and the Greens also agreed a pro-Remain pact across 60 seats.
Labour and the Lib Dems did not agree on a pact, despite calls for them to find an agreement.
The Lib Dems want to cancel Brexit entirety, while Labour plans to hold a second referendum on a negotiated deal.