"... as the local elections showed, they are ... are on course for the type of victory last seen by (Labour's) Tony Blair and Margaret Thatcher when they were at their peaks", said Adrian Drummond of pollsters Opinium.
UKIP lost all but one of the more than 100 council seats it held, as voters switched to the Conservatives now that UKIP's main goal had been achieved.
Theresa May's Conservative Party gained control of Warwickshire, Lincolnshire and Gloucestershire while the Labour Party and UKIP recorded losses as counting continues in local and mayoral elections in the United Kingdom, local media reported.
Conservatives won the West of England metro mayor contest, while Labour claimed the mayoralties in Greater Manchester, won in the first round of voting by former cabinet minister Andy Burnham, Liverpool, Doncaster and North Tyneside.
Voters in Nottinghamshire went to the polls on Thursday (May 4) as part of 88 council and mayoral elections being held five weeks before the general election.
Jeremy Corbyn suffered a major setback in his hopes of mounting a challenge for No 10 as Labour haemorrhaged scores of council seats. We know this is no small task, it is a challenge on a historic scale.More news: Russian FM mocks US media over intelligence-sharing reports
"If the Labour, Lib Dem and Green vote is split then Conservatives will win", he warned.
As Ukip shed 109 councillors while holding a solitary seat in Lancashire, leader Paul Nuttall said the party was "a victim of its own success" over Brexit. The UKIP suffered a huge defeat - losing 145 seats and winning only one - virtually wiping them out.
Al Jazeera's Barnaby Phillips, reporting from Westminster, said it was striking that the Conservatives had made gains in Scotland, pushing Labour - once the dominant political force in Scotland - into third place, behind the Scottish National Party and the Conservatives.
Cllr Truelove wondered if, with a general election around the corner, voters would be less inclined to vote "politically" in the local elections, instead focusing more on the quality of the local candidate than they perhaps would have done had Theresa May not called a snap vote for June 8.
But the party lost 382 councillors and gave up control of seven authorities across England and Wales, with analysis suggesting that Mrs May can expect a Commons majority of at least 48 on 8 June. A telephone poll by Ipsos Mori placed the party on 49 per cent, with Labour on 26 per cent, the Lib Dems on 13 per and Ukip on four per cent.
Labour also lost control of Glasgow City Council, which it has controlled since 1980, and the SNP is expected to become the biggest party there.