The spread of the Conservative losses led one former minister to claim there was "no such thing really as a safe Tory seat any more".
But the prime minister appeared set to cling on until the general election, with rebels in his own party lacking the support to oust him.
The polling expert Prof John Curtice of Strathclyde University described the national picture as "one of the worst, if not the worst" performances by the Conservatives in four decades.
The party is expected to end up losing up to 500 seats when all votes are counted, with Labour advancing in areas of both the "red wall" in northern England won by the Tories under Boris Johnson and the traditional southern Conservative heartlands.
The Labour leader, Keir Starmer, hailed "seismic" results including winning a landslide byelection in Blackpool South, with the third largest swing since the second world war, as well as mayoralities in the East Midlands, North East and North Yorkshire, which covers Sunak's own constituency. Labour also ousted a number of Tory police and crime commissioners, and took control of at least seven new councils, including in Buckinghamshire, Hampshire, Essex and Sussex in the south of England.
Overall, Starmer's party won at least 170 new council seats to reach a total of more than 870 seats, while the Liberal Democrats also made gains in the south and west, adding at least 60 more seats to reach at least 350.
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