Labour has lost control of two key councils in its traditional heartlands, conceding power to the Conservatives in Bolton and Darlington for the first time in 40 years.

The party made significant losses in the local elections last week, in what councillors described as a backlash over local issues and the Brexit stalemate.

In Darlington, which has elected a Labour MP at every poll since 1992, the party lost its grip on power on Friday when the Conservatives agreed a power-sharing deal with smaller parties.

In Bolton, Labour lost seven seats and conceded control of the council to a Conservative administration, propped up by independents and smaller parties such as the Liberal Democrats and Ukip.

The defeats come a week after Labour had a net loss of 80 seats in local elections dominated by the Brexit impasse. The results, while disappointing for Jeremy Corbyn’s party, were dwarfed by the loss of more than 1,300 Tory seats across the country.

In Bolton, which voted 58% to leave in the 2016 EU referendum, Labour acknowledged its setbacks in the elections but blamed voters’ lost confidence in politics on Brexit and government cuts.

The Labour group pledged to “listen and do our utmost to rebuild our relationship with the people of Bolton” and maintained that the Conservatives, which made a net gain of only one seat, did not have a mandate.

“The Conservatives have been out of power in Bolton for 40 years and there is clearly a reason why Bolton people have continually rejected them,” the group said.

David Greenhalgh, the leader of the Conservative group, said voters had lost confidence in Labour and it was “unbelievable” the local party “refused” to accept that. “These were the worst elections for Bolton Labour probably in the history of the metropolitan borough,” he added.

In Darlington, Labour lost nine councillors compared with 2015 as part of a surprising shift to the Tories, who gained five seats to become the largest party on the council. The Conservatives look likely to take control of the council for the first time in a generation after agreeing a deal in principle with the Lib Dems and independents.

Cllr Kevin Nicholson, the leader of the independents group on Darlington council, said Labour had been punished because it “stopped listening to people and became complacent” on local issues.

“After 28 years of Labour rule, the connection between the people and the politicians was lost,” he said. “These are areas where you wouldn’t, 10 years ago, have worn a blue rosette in the streets.”

Peter Gibson, a solicitor who was selected in December to be the Conservative parliamentary candidate for Darlington in the next general election, said he had spearheaded a Tory campaign that contested 46 out of 50 council seats – far more than in previous local contests.

“For the past 30 or so years, the Tories haven’t fielded anywhere near a full slate of candidates, reasoning, ‘We’re never going to win in certain wards, so let’s just concentrate on where we can win.’ When I was selected I said, ‘We’re going to do this properly. We’re going to give people all over Darlington the chance to vote for us.’”

The Conservative campaign hammered Labour on the state of the town centre in Darlington and particularly its decision to outsource litter enforcement to a private company.

• This article was amended on 14 May 2019. An earlier version referred to Bolton and incorrectly described the Conservatives as “ the largest party on the council”.