Labour MPs are increasingly optimistic that the party will hang on to its seats in two crucial byelections on Thursday, as it prepares for a race to the wire with Ukip in Stoke-on-Trent Central and the Conservatives in Copeland.

Despite poor national polling for both Labour and Jeremy Corbyn, party campaigners in the West Midlands and Cumbrian constituencies believe incumbency and local issues including the NHS are likely to lead to victory.

In Stoke, Labour activists have taken heart from the troubled campaign of Paul Nuttall, the Ukip leader, who faced questions over his residency in the constituency, failed to name one of the six pottery towns in the seat and admitted he had not lost close personal friends at Hillsborough despite claims on his website.

Vernon Coaker, the Labour MP for Gedling, who canvassed there last week, said: “We are positive. It’s been a tough fight with Ukip but Paul Nuttall’s claims have come up on the doorstep. All of those things about Hillsborough and his home address have been raised. We have taken the battle and the fight to Ukip, we haven’t just stood back and let them say things. We are also highlighting the impact of a Tory government on Stoke.”

The seat is especially unpredictable because of the expected very low turnout but two Labour MPs said they believed they would hold on to Stoke even though there was “no wild enthusiasm for Labour” and a fair degree of hostility towards Corbyn.

Toby Perkins, Labour MP for Chesterfield, said: “The sense that Paul Nuttall has damaged his own campaign is a very real one and a sense of ‘is it a protest worth risking?’ That has sharpened over the last couple of days.”

Labour HQ sources were also optimistic about holding Copeland after the prime minister went to the seat last week without offering any guarantees about the future of maternity care or nuclear power – two dominant issues in the Cumbria constituency.

Another Labour MP who has just returned from Copeland said: “If we win, we will have ground out a victory in those two seats because of the hard work of activists on the ground despite the leadership. I hope Jeremy and his supporters will be gracious enough to recognise that. What we have is a ground game.”

Paul Nuttall has made a string of errors during his campaign in Stoke. Photograph: Joe Giddens/PA

Speaking at the Labour local government conference in Warwick on Saturday, Corbyn said the byelections were a chance to “send a message to a Conservative government that puts the rich first but neglects the sick, the elderly, and those with disabilities”.

Commenting on Tony Blair’s call for a cross-party movement to halt Brexit, Corbyn said the speech had been “unhelpful”. He added: “The referendum gave a result, gave a very clear decision on this, and we have to respect that decision, that’s why we didn’t block article 50. But we are going to be part of all this campaigning, all these negotiations about the kind of relationship we have in Europe in the future.”

He added: “The referendum happened, let’s respect the result. Democracy happened, respect the result.”

The national picture for Labour is still difficult. According to the latest Opinium/Observer polling of 2,000 voters last week, support for Labour dropped by three percentage points to 27%, while backing for the Conservatives rose three points to 40% in the month in which Theresa May’s Brexit bill has passed through the Commons with the help of the Labour frontbench. The Lib Dems were unchanged on 8% and Ukip also remained on 14%. Corbyn’s personal ratings dropped to a net minus 35, matching those of Michael Foot at the same stage of his leadership in the early 1980s. May’s net ratings rose to plus 17.

Corbyn visited Stoke on Saturday and has made two visits to Copeland earlier in the campaign. His leadership is unlikely to come under further pressure from MPs unless both seats are lost on Thursday, but the next test for the party will be local council elections in May.