An ORB International poll for the Telegraph put Labour two points up since last week on 34 per cent.
Although Mr Corbyn’s party trailed Tories – on 46 per cent – by 12 points, it matched Labour’s best rating in a mainstream poll this year and added weight to the idea that its campaign is winning over voters.
Crucially, it puts Labour comfortably above the 30.4 per cent share of the vote achieved by Ed Miliband in 2015, a benchmark which some supporters argue should remove pressure on Mr Corbyn to quit if he fails to win power.
Meanwhile, a second poll by Opinium for the Observer put Labour up one point on 33 per cent to Tories’ 46 per cent.
And Mr Corbyn said: “This message is getting through. Get on any bus, get on any train, go in any cafe, talk to people.
“The whole discussion and the whole debate is unravelling from the Tory point of view, because people are saying ‘Hang on, why are so many young people in such stress?
“Why are so many older people being threatened by this Government? Can’t we as a society, as a country, as a people do things differently and better?”
Mr Corbyn accused Theresa May of fomenting a “war between the generations” by playing off old against young in her election manifesto.
Meanwhile Shadow chancellor John McDonnell told activists in Birmingham there was “all to play for” in the remaining three weeks, declaring: “Let’s get out there and win this election, let’s carpe diem (seize the day), let’s seize this opportunity, with courage and determination, we can win this election despite what they throw at us.”
But the Prime Minister fought back by saying that a shadow cabinet row over the renewal of Britain’s Trident nuclear deterrent showed that Mr Corbyn could not be trusted to defend the country.
Mrs May too played up the prospect of a close result on June 8, as she urged supporters not to allow Corbyn into Downing Street on the back of a coalition of opposition parties.
Writing in the Daily Mail, the Prime Minister said it was a “cold, hard fact” that if her party lost six seats, Mr Corbyn could take power in a scenario which should “scare us all”.
After shadow foreign secretary Emily Thornberry suggested that the future of Trident could be up for grabs in a post-election Labour defence review, Mrs May said it was clear that a Corbyn-led administration would not be “unequivocally committed” to Britain’s independent nuclear deterrent.
“They would not be able to defend this country,” she told Tory activists in west London. “A Jeremy Corbyn-led Labour government could not be trusted with the defence of our country.”
Mr Corbyn was forced to restate his commitment to renewing Trident, with a senior aide insisting that Labour was committed to a continuous at-sea deterrent “come what may”.
Additional reporting by Press Association