Mrs May said the Copeland result showed that the Conservatives are the party "listening and responding" to working people across Britain.
Conservative Trudy Harrison scored a spectacular victory in Copeland on Friday morning, taking the seat from Labour for first time since the 1930s, with a majority of 2,147. The Tory candidate, Trudy Harrison, won with 13,748 votes to Ms Troughton's 11,601, increasing the Conservative vote share in the constituency by 8 points to 44 per cent.
Thousands of people in the area are employed in the nuclear industry, and Mr. Corbyn has a long record of campaigning against nuclear power.
"The party is faced with the problem of a leader who is simply not acceptable to a large number of people who would normally vote Labour", Mr Winnick said.
Copeland, in Cumbria, has a clear identity as a town that powers the rest of the United Kingdom, with 10,000 of its jobs reliant on the nuclear industry at Sellafield and a proposed plant to replace it, Moorside, which could provide up to 20,000 new jobs.
Although Labour held on in the Stoke-on-Trent Central by-election, seeing off UKIP leader Paul Nuttall, it saw its vote share cut while the Tories increased theirs.
Corbyn said: "Labour's victory in Stoke is a decisive rejection of UKIP's politics of division and dishonesty". Pittella reassured Corbyn that the S&D group would resist the Conservative Party's "ultra-hard Brexit", instead the S&D Group are calling on a "fair Brexit".
In the case of Copeland for example, Labour MP Jamie Reed resigned from his office in December previous year.
Mr Corbyn said both constituencies had been "let down" by the political establishment.
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The general secretary said this afternoon: "The blame for these results does not lie exclusively with Jeremy Corbyn, but he must take responsibility for what happens next".
"We've always said the Labour party is not just one person, whoever the leader has been".
Ukip were confident that Hunt's majority of 5,000 at the 2015 general election was vulnerable given Stoke's vote to leave the European Union and Labour's recent struggles.
"Word had got out that Jeremy was not in favour of nuclear power - that isn't true, that is what you call "fake news" and we were having great difficulty fighting that", said the shadow foreign secretary. "So I think we were pretty upset to lose that seat", she said.
We have a real problem in the North and the Midlands because of the rise of Ukip, and I don't think it's really do to with Ukip.
This week's by-elections were required because the sitting MPs - both Labour - quit, for jobs outside Parliament.
More significantly, the by-elections indicate that Mr Corbyn, an old party operative who lives in an expensive suburb of the British capital, holds no attraction for core Labour voters, who are largely concentrated in the working-class central and northern regions.
However, with Labour divided over Mr. Corbyn's leadership and Brexit, the bookies strongly suggesting it would fall to the Conservatives this time.
Appearing on Channel 4 News, Baroness Chakrabarti was asked if she would like the Labour leader to face a general election "sooner rather than later".