Britain’s Conservative Party suffered sweeping setbacks on Friday in local elections that are viewed as a barometer for how the party will perform in a coming general election and a key test for the embattled prime minister, Rishi Sunak. With most of the results announced by Friday evening, the Conservatives were on course for one of their worst performances in a set of local elections since the 1990s. The party has lost more than 400 seats so far, including six in Hartlepool, a town in northeast England emblematic of the expanded political territory it had claimed since Brexit, and is now losing to a resurgent Labour Party. The Conservatives did score one notable victory in a closely watched race for mayor of Tees Valley, also in northeast England, where the Tory incumbent, Ben Houchen, held on, eking out a reduced majority. Almost everywhere else, however, the picture was bleak for the Conservatives, who have trailed the opposition Labour Party by double digits in national polls for 18 months and face the prospect of a landslide defeat in a general election.