Labour expects to win the Corby by-election with a majority of more than 4,000, senior party sources said.

The Tory candidate Christine Emmett is expected to lose out to Labour's Andy Sawford, who needs to overturn the Conservative majority of 1,951 votes.

A poll drubbing in the seat, which was held by Louise Mensch, would give Labour its first Tory by-election scalp since 1997 and prove embarrassing for Prime Minister David Cameron.

A senior Labour source suggested the party could secure a majority of 4,000, with the Tories in second. "We are increasingly optimistic about a good win in Corby," the source said. "Turnout is looking as if it will be 45% and the Tory and Lib vote has collapsed."

Mrs Mensch, who quit the seat in August so she could move to New York for family reasons, said she would accept responsibility for an election loss. Taking to Twitter, Mrs Mensch said: "Election result will not be a verdict on either Christine, or the Conservatives, but only on the decision I took to step down mid-term."

Conservative Party co-chairman Grant Shapps took a swipe at Mrs Mensch, saying he believed MPs who stood for election "should stay there". He told Sky News: "I saw a tweet from her saying that actually she understands why people would be miffed. I have been there and I've heard what people say on the doorstep - MPs should stay the course. I think it would be very helpful to stand for the full parliament."

Mr Shapps said anything under an 11,000 majority in Corby would mean Labour leader Ed Miliband was "under pressure". He added: "Just to get a measure of this, Crewe was a mid-term election in the last parliament for us. If Labour were to repeat what we did in Crewe, to go on and win the election, they'd be looking for about an 11,000 majority based on the turnout they have had."

Meanwhile there have been swings towards Labour as the party held its two seats in the other two parliamentary by-elections being held, but the results were tempered by a low turnout of voters.

Manchester Central and Cardiff South and Penarth were both held by Labour as expected but the Manchester Central result was marred by a turnout of just 18.16%, the lowest in a parliamentary by-election since the Second World War. In Cardiff South, turnout was 25.65%.

Stephen Doughty claimed Cardiff South and Penarth with 9,193 votes, while Lucy Powell won in Manchester Central with 11,507 votes. In Manchester Central, the swing away from the Liberal Democrats was 16.77%. For Tory candidate Matthew Sephton, the result was so disappointing he lost his deposit as he only managed 754 votes, less than 5% of the total turnout.