As Jeremy Corbyn claimed his message was "getting through" to voters, four polls for the Sunday newspapers put Labour between 35% and 33%, up significantly on the scores as low as 26% it was recording early in the campaign.
The Tory advantage was narrowed to just nine points in one survey by YouGov for the Sunday Times, the first time it has been in single figures in a mainstream poll since Theresa May called the snap election on April 18.
Although the figures would deliver a comfortable Tory majority if repeated on June 8, they will bolster Labour insiders' belief that Mr Corbyn's campaign is making inroads into Theresa May's support following her poorly-received policies on social care for the elderly.
Crucially, a result on these lines would put Mr Corbyn comfortably above the 30.4% vote share achieved by Ed Miliband in 2015, which some supporters argue should be seen as a benchmark of whether he should stay on as leader.
One Labour insider characterised the mood in the Corbyn camp as "extremely positive", after the Labour leader attracted a crowd of thousands to a rally in super-marginal Wirral West and then heard his name chanted in approval by rock fans when he appeared on stage before the Libertines at a music festival at Tranmere Rovers football ground in Birkenhead.
The 35% support for Labour recorded by YouGov for the Sunday Times is the best rating for the party since March last year before the divisive EU referendum and the abortive challenge to Mr Corbyn's leadership.
The poll put Tories on 44%, though Mrs May's party was on 46% in separate surveys by ORB International for the Sunday Telegraph, Opinium for the Observer and Survation for the Mail on Sunday.
The Survation survey, conducted entirely after Thursday's Tory manifesto launch, found 28% of voters said they were less likely to vote Conservative because of the social care package, branded a "dementia tax" by opponents.
Just 28% of those questioned approved and 47% disapproved of the scheme, which would allow the value of a person's home to be included in their assets when recouping the cost of care at home, with protection for £100,000 of the total.
Conservatives took the fight to Labour over Mr Corbyn's tax plans, with a claim almost five million homes could be affected by his promise to lower thresholds for inheritance tax.
Labour's manifesto promised to reverse inheritance tax "giveaways" introduced by the Conservatives, but did not say what threshold the party would set for the 40% levy.
Reversing George Osborne's reforms, which have lifted it to £850,000 and are due to see it rise further to £1 million by 2021, would take it back down to £650,000.
Chancellor Philip Hammond claimed Labour would go further and impose the tax on all homes worth £425,000 or more, which would catch 3.9 million of the 25 million properties across England and Wales.
Rising house prices could be expected to increase the total to 4.9 million within five years if the threshold stayed at that level, said Tories.
If the Conservative figures are right, some 51% of homes in London, 48% in Cambridge, 46.7% in Guildford and 38.7% in Oxford would be liable, the party said.
Overall, some 15.3% of properties in England and Wales would be hit, with the lowest impact felt in Torfaen in south Wales (0.2% of properties), Merthyr Tydfil (0.3%) and Neath Port Talbot and Barrow-in-Furness (0.6%).
Mr Hammond said: "Jeremy Corbyn wants to hit family homes with a bombshell of new taxes.
"Ordinary families across the country will suffer because of his nonsensical policies.
"People who have worked hard all their lives, saved and improved their homes will now be hit with this punishing family homes tax."
Meanwhile, Mr Corbyn made a further push to win over pensioners by highlighting five Labour pledges for older people, in a sign of his belief that the Tory manifesto, which also included plans to ditch the triple-lock protection on the state pension and means-test winter fuel payments, has weakened the Conservatives' formerly firm grip on the grey vote.
The Labour leader said he would keep the triple lock, winter fuel payments and free bus passes and would halt planned rises in the retirement age beyond 66, as well as ensuring "justice" for women born in the 1950s affected by the equalisation of women's and men's pension eligibility.
"Not satisfied with plunging our social care system into crisis, Theresa May's nasty party has promised more attacks on older people," said Mr Corbyn.
"Theresa May and the Conservatives won't stand up for pensioners, their only concern is their billionaire friends.
"Labour is proud to stand up for the many, not the few."
:: The ORB poll for the Sunday Telegraph put Conservatives on 46%, Labour on 34% and Liberal Democrats on 7% following interviews with 2,040 voters on May 17 and 18.
:: Opinium's survey for The Observer had Tories on 46%, Labour on 33% and Lib Dems on 8%. The company questioned 2,003 voters on May 16 and 17.
:: Survation's poll for The Mail On Sunday put the Tories on 46% and Labour on 34%, with Lib Dems trailing on 8%. Survation questioned 1,017 adults on May 19 and 20.
:: For the Sunday Times, YouGov had the Conservatives on 44%, Labour on 35% and Lib Dems on 9%. YouGov polled 1,005 adults on May 18 and 19.