British Prime Minister Theresa May's Conservatives secured a landmark victory in a parliamentary by-election on Friday, boosting her hand ahead of upcoming Brexit negotiations as her rivals suffered damaging poll setbacks.

The Conservatives captured the north western region of Copeland that Labour have held since 1935, the first by-election gain for a governing party for 35 years and a result which piles pressure on the opposition's under-fire socialist leader, Jeremy Corbyn.

In the central English seat of Stoke-on-Trent, Paul Nuttall, leader of the populist anti-EU UK Independence Party, failed to overturn a Labour majority despite almost 70 percent of the city's voters backing leaving the bloc at last year's referendum, casting doubt on his future too.

The Conservatives also increased their share of the vote in Stoke from the 2015 election.

The two results point to May's tightening grip on political power following the Brexit vote, and will be used as evidence that her strategy of pursuing a clean break with the EU has stemmed rising right-wing populism without denting her ability to take votes from an increasingly left-wing Labour Party.

Although Labour avoided the worst-case scenario of two defeats, Corbyn is likely to face renewed criticism.

"The result ... is a disaster for us. We should not try to insult people's intelligence by suggesting other than that," Labour lawmaker John Woodcock told BBC radio.

Many Labour parliamentarians worry Corbyn's leadership is damaging their fight for a "softer" Brexit, with closer ties to the EU's single market, while his leftist agenda is making the party unelectable before a 2020 national election.

"We’re actually on course to an historic and catastrophic defeat," Woodcock said.

"This is a time where the country really needs an effective opposition and they need an alternative to what I think is a very damaging approach the Conservative government is taking on the issue of leaving the European Union."

Despite long-running unrest within the upper ranks of his party, Corbyn is unlikely to face a fresh leadership challenge because he retains strong support among the grassroots Labour members who re-elected him last year after a botched coup.

"To win power to rebuild and transform Britain, Labour will go further to reconnect with voters, and break with the failed political consensus," Corbyn said in a statement after the result.

UKIP STUTTER

In Stoke, UKIP were unable to capitalise on the anti-establishment sentiment it tapped so successfully when persuading voters to leave the EU last year, despite pouring resources into a campaign waged on fertile Brexit territory.

The party's former leader and best-known figure Nigel Farage had warned last week the Stoke vote was vital for the future of the party, beset by in-fighting since the Brexit vote.

"UKIP's time will come ... there's a lot more to come from us, we're not going anywhere, I'm not going anywhere," Nuttall told reporters after the result.

A campaign dogged by personal gaffes risks reigniting feuding within the party, which has struggled to break into mainstream politics despite playing a pivotal role in forcing the government to call an EU referendum and the subsequent campaign to leave the bloc.

"If you want to be an electoral force and a political force in this country you have to be able to win by-elections in difficult circumstances as a third party," Rob Ford, a politics professor from Manchester University and an expert on UKIP, told Reuters

"If they can't do that even in the most propitious of seats people will start to have questions."