Progressive voters could push Reform UK into fourth place and put Labour within touching distance of a majority if tactical voting is widespread at the next election, a major poll has found.

Andy Burnham is beginning to attract a significant number of left-leaning voters back to Labour, motivated by a desire to stop Nigel Farage, the results suggest.

The poll of more than 8,000 voters, shared with the Guardian, suggests a widespread openness to voting tactically. It also shows the prime minister's most successful electoral strategy would be to unite the centre and left bloc of voters, while the right remains split.

It would be a marked contrast to the tactics of Keir Starmer's Labour before the 2024 general election, when the party tried to attract more conservative older voters. Such a tactic would be likely to unsettle some in Labour, given the same strategy was deployed for Ed Miliband's failed bid in 2015, albeit before Reform's arrival as a major electoral force.

The poll on the eve of Labour's annual conference in Liverpool shows a significant shift of left-leaning voters towards Burnham's Labour and will encourage those in the party who are thinking of gambling on an early election while Reform's ratings are ebbing and while leftwing parties such as the Greens appear to be losing momentum.

Twice as many voters have returned to Labour from the left as from the right since April.

The previously unreleased research, including a seat-by-seat MRP model, was conducted by Survation and the progressive activist site 38 Degrees in Burnham's first month as prime minister.

It suggests Labour would be the largest party in parliament if an election took place today, on 272 seats, a four-point lead. This would mean achieving 42% of parliamentary seats with 28% of the vote.

Reform would become the official opposition on 153. This represents 24% of seats – the same as its vote share. The Conservatives would fall to third place with 85.

Two hundred seats are tight marginals decided by under five points, meaning a two- to three-point swing could move about 100 seats that are likely to decide a future election. But in a sign of the volatility of the polls, a far higher percentage of voters are open to tactical voting in those seats when they cite their preferred party.

If voters are prepared to switch to one of the two frontrunners in their seats, rather than their preferred party, then Reform UK's seat count would fall dramatically, favouring Labour and the Conservatives.

About 18% of voters who live in a seat where tactical voting would make a substantial difference say they are willing to do so but are not yet doing so. If those voters decided to vote tactically, Reform UK would be reduced to 62 seats, giving Labour 319 – six short of a majority.

Of the 91 seats where Reform would cease to be the most likely winner, 46 would go to the Conservatives and 43 to Labour. The projection is unlikely to be exact at this stage in the electoral cycle.

Reform's chances of winning fell by more than 50 points in 59 seats. Among these are the Wrekin, Torridge and Tavistock, and North West Cambridgeshire – all of which have Reform as the most likely leader under the "normal" assumptions but lose out to the Conservatives under a scenario with more tactical voting.

In 2024, the now-chancellor, John Healey, held Rawmarsh and Conisbrough with 49% of the vote, with Reform in second place on 28.6%. The base modelling of the MRP indicates that Reform could win a tight race in the seat, with a 51% chance, but this plummets if tactical voting increases, with a 76% chance of Labour holding the seat in this scenario.

In Bassetlaw, Reform could lose even as its own vote share rises from 35% to 40%, because tactical voting would lift Labour further – from 32% to 40%. The Conservatives, Liberal Democrats and Greens would lose supporters if this switching took place. The forecast estimates that the winner would shift from Reform, with a 77% chance, to Labour, with a 58% chance.

Newark, held by the Conservative-turned-Reform MP Robert Jenrick, is forecast to flip to the Conservatives under both scenarios, although under heavier tactical voting the chance of a Conservative win increases from 68% to more than 99% should Labour backers vote Conservative to stop him.

Damian Lyons Lowe, Survation's chief executive, said: "Estimating tactical voting is a complex consideration, but the mechanics here are simple. Four in 10 voters are currently backing a party that can't finish in the top two where they live and are willing to vote tactically.

"But when we ask whether they would lend their vote to the stronger local contender in a two-horse race, around half said yes. That gap – worth some 18 points of the national electorate – is an enormous untapped reservoir for parties looking to squeeze voters.

"Should these voters act as they say, our model shows Reform falling from second place to fourth, losing around 90 seats, despite its own vote share actually going up. Reform-leaning Conservatives will consolidate too. Reform doesn't collapse; it risks being outnumbered, seat by seat, by voters coordinating around whoever is best placed locally on the left and right."

The prediction is also complicated by the sheer number of seats Labour won in 2024 from the Conservatives where the party has been polling as low as third over the past year. Progressive voters living in seats such as Labour-held Southend would be unlikely to opt to vote for the Conservatives, even if they were technically the best placed to beat Reform at the next election, showing the limitations of predictions around tactical voting.

The poll also suggests Labour is gaining considerable numbers of voters back from other leftwing parties, but not from Reform. The share of Labour's lost 2024 voters going to the Greens, Liberal Democrats, Plaid Cymru or the Scottish National party has fallen from 60% to 46%; but on the right, of those lost to Reform or the Tories, it has fallen from 27% to 24%.

Veronica Hawking, the campaigns director at 38 Degrees, said the polling indicated a far more optimistic public mood than before the Labour conference last year, but there was also significant expectation that Burnham needed to deliver.

"There are signs of optimism and even hope, but what has not changed is the way voters are crying out for bold action, fast," she said. "The results show a huge amount of common ground between voters, especially when it comes to the cost of living. Voters who have moved in different directions since the general election two years ago are united by the fact that action on the cost of living crisis will have the single biggest bearing on their future vote."