The Conservatives are making plans to go after seats in Labour’s traditional heartlands after winning mayoral contests in the north-east of England and the West Midlands as well as seizing control of 11 more councils.

Theresa May insisted she was “not taking anything for granted” before the 8 June general election but the local and mayoral results showed the Conservatives benefiting from the collapse of Ukip’s vote across the country, including in areas of historical weakness.

May’s strategists have the confidence to go on the attack in June after the party swept up more than 500 new council seats in England, Wales and Scotland. The Tories also pulled off a shock mayoral win in Tees Valley, a formerly deeply Labour area in the north-east of England, and a narrow victory in the West Midlands, where former John Lewis boss Andy Street beat former MP Siôn Simon to become mayor.

Street, who became the favourite despite the strength of Labour in the Midlands, said he hoped the victory was the birth of a “new urban agenda” for the Conservatives.

The Tories already dominate councils in the south, but the party went on to displace Labour as the largest party in Nottinghamshire, Lancashire, Cumbria, Northumberland and Derbyshire.

Anne-Marie Trevelyan, a Conservative MP for Berwick-upon-Tweed, praised the result in Northumberland as the north-east of England had not had a Conservative-run council for decades. Her party was denied an outright majority by one seat, after a tie with the Lib Dems led to the result being decided by drawing lots.

“My worry throughout the whole thing was that we were going to see swings to Labour in the Midlands, but in the north-east, really? It has been such a solid tribal Labour vote,” Trevelyan said.

“I wasn’t sure if people could bring themselves to vote Conservative because we still have a mining heritage. But Theresa gives them confidence. On the doorstep, day after day, it is confidence that Conservatives are conservatives with a small ‘c’, who believe in financial prudence, responsibility, getting on. Theresa embodies that. The north-east voting population is very conservative but they just called it Labour in the past.”

In Scotland, the party became the largest in six of 32 areas, suggesting Ruth Davidson, the Scottish Tory leader, has begun a revival after decades in the wilderness.

The Tories also made gains in Wales, taking Monmouthshire council, but the results were not as good as opinion polls had indicated.

Conservative MPs were particularly surprised by the victory in Tees Valley, which is overwhelmingly represented by Labour MPs. One minister simply texted: “Tees Valley: amaze balls.”

Ben Houchen, the new Tory mayor for Tees Valley, said in his victory speech there was “a massive trend towards the Conservatives” in the region. “We have started to turn the Tees Valley blue,” he added

It is understood Tory MPs in safe seats are now being paired with Labour-held marginals across the north of England and Midlands with the aim of breaking old tribal voting allegiances to Labour at the general election.

Conservative candidates are receiving help in target constituencies in parts of Yorkshire, Lancashire, the West Midlands and even the north-east, particularly where the Ukip vote in 2015 was larger than the Labour majority.

Speaking after the result in the Tory-Labour marginal of Brentford, May insisted the stakes of the election were high because “there are bureaucrats in Europe who are questioning our resolve to get the right deal” on Brexit.

Pressed on whether her warnings that there could be a Corbyn-led coalition were credible, she said Corbyn could pull off a victory and the polls could be wrong.

“I don’t take anything for granted and if you look what happened in the last couple of years, we saw the opinion polls got in wrong in the 2015 general election and last year in the referendum and of course Jeremy Corbyn has pointed out he was a 200/1 chance for the Labour leadership. The general election will be won on the day by real people going out and casting real votes. I want to earn the support of the people to strengthen my hand.”