The governing centre-right party is still on course for a comfortable victory, but no longer enjoys the 20-point lead that provoked talk of a landslide at the start of the campaign.
Newspaper commentators warned of a backlash against May's proposed plan to address the rising cost of social care for the elderly, which could see higher bills for many people.
"Tory wobble as cuts for elderly slash May's lead," headlined the Sunday Times, as a YouGov poll found the party's lead halved in a week.
YouGov found 40 per cent of voters opposed the social care plan, and 35 per cent supported it.
Foreign Secretary Boris Johnson said it was "necessary" to meet the challenges of an ageing population.
"I think it is a mark of Theresa May's bravery and candour with electorate that she is doing this," he told ITV television.
May called the snap election in April, saying she wanted a mandate to go into the negotiations on taking Britain out of the European Union.
Its leader Jeremy Corbyn claims his plans to nationalise the railways, raise taxes and invest in public services are widely popular.
An ORB/Sunday Telegraph survey put the Conservatives on 46 per cent, unchanged from last week, and Labour up two points on 34 per cent.
An Opinium/Observer poll, taken after Labour's manifesto launch but before the Tories', put May's party down one point in a week at 46 per cent, and Labour up one point at 33 per cent.
A Survation/Mail on Sunday poll put the Conservatives at 46 per cent and Labour at 34 per cent. It is based on new methodology, so cannot be compared to previous results.
The pro-European Liberal Democrats have fallen from around 11 per cent to around eight per cent.
The UK Independence Party (UKIP), a once potent force which has struggled to stay relevant since last year's referendum vote for Brexit, is languishing at between three and seven per cent.
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