The Ipsos Mori poll found 61 per cent of voters saw Mrs May as the “most capable” of the leaders of the main political parties, against 23 per cent for Labour’s Jeremy Corbyn.
The ranking is the strongest the pollster has recorded since it began asking the question in the 1970s, outstripping Mrs Thatcher’s peak of 48 per cent shortly before her landslide defeat of Michael Foot in 1983 and Mr Blair’s high point of 52 per cent ahead of his emphatic 2001 election victory over William Hague.
The poll put Conservatives on 49 per cent - up six points since last month - against Labour’s 26 per cent (down four). Liberal Democrats were unchanged on 13 per cent, while Ukip slumped from 6 per cent to 4 per cent and Greens were down from 4 per cent to 1 per cent.
If repeated at the ballot box, it suggests Mrs May is heading for a majority comfortably over 100 seats on June 8.
:: Ipsos Mori interviewed 1,004 adults across Great Britain between April 21 and 25.