The survey – carried out on behalf of the Labour-aligned Fabian Society – found the opposition is doing 10 points better in these seats than the national average.
Support for Labour is at 52 per cent in the 150 marginals identified by the think tank, with the Conservatives way behind on 18 per cent.
It comes as a separate YouGov survey shows that the Tories’ hard-right rivals Reform UK have climbed to their highest-ever level of backing at 13 per cent – as support for Mr Sunak continues to get squeezed.
Ben Cooper, the Fabians’ research manager, said the think tank’s previous analysis of marginals showed the “huge mountain” Labour still had to climb.
“This new polling data shows the party may be able to turn a mountain into a molehill,” he said. “However, Labour is right to argue that there is no room for complacency.
The expert added: “The significant portion of ‘don’t know’ voters and levels of support for Reform shows that there is still a lot of work to do between now and poling day to turn an opinion poll of marginal seats into real election results.”
Since the 2019 election, there is a national swing from the Tories to Labour of 17 percentage points – but the swing in these key seats is an even higher at 22 points.
But the think tank said the high levels of people still telling pollsters they “don’t know” who they will vote for, and the improved showing by Reform, meant there was no room for complacency for Labour.
The latest YouGov voting intention survey shows Reform up one point on 13 per cent of the vote. Leader Richard Tice said his party was “closing in” on the Tories – since they are just seven points behind Mr Sunak’s party on 20 per cent.
Labour remains unchanged on 47 per cent, while the Liberal Democrats are languishing on eight per cent on the vote.
It emerged that one of Mr Sunak’s former advisers – who quit his role last year after becoming dispirited – is now working with a group of rebels plotting to replace the PM.
In a statement Will Dry – revealed to be working with a small group of right-wing former advisers and MPs – said the Tories were heading “for the most almighty of defeats”.
He also warned: “And if [Nigel] Farage comes back [to lead Reform], the Conservative party won’t exist by Christmas.”
Mr Dry’s comments follow an op-ed by senior MP Sir Simon Clark that was published on Tuesday, which said Mr Sunak’s leadership was “uninspiring” and called for him to step down.
Sir Simon responded to the flak he received from fellow Tory MPs – describing himself to a disliked man shouting “iceberg” as he appeared to compare the Tories to the Titanic.
“I totally respect the strong views that something like this evokes,” he told BBC News. “No one likes that guy that’s shouting ‘iceberg’, but I suspect that people will be even less happy if we hit the iceberg.
“And we are on course to do that. That is the point that I need to land with colleagues respectfully and calmly … I really worry that we’re on course for a shattering course.”