The Labour leader stressed that his party had to “earn” every vote and that many voters in the North East constituency were focused on “jobs, jobs, jobs,” with a local power plant set to close and steel jobs also under threat.
With the threat of a historic defeat on Thursday in Hartlepool, a seat Labour has held for 47 years since its creation, Sir Keir told LBC Radio: “It was always going to be tough.”
He emphasised that Labour had a “mountain to climb” after its 2019 election disaster under Jeremy Corbyn.
Watch: Local elections - how to measure success and failure for each party on 6 May
“I never thought … that the Labour Party could go from the devastating defeat in 2019, the worst since 1935, and mend all that in about a year or a year-and-a-half,” he later told ITV’s Good Morning Britain.
Asked if he would step down if Labour had a bad night, he added: “We are fighting for every vote into this election.
“I have a burning desire for a better future for our country, and I want this Thursday to be the first step towards that future.”
Speaking on Monday night to thousands of Conservative activists across the country, Boris Johnson stressed it was still a “massive challenge” for his party to win Hartlepool which is set to benefit from a new “freeport” being established on Teesside.
He was due to say: “It’s important for people to understand this is not a seat that Conservatives have ever held.
“This is the stamping ground of Peter Mandelson.
“It’s very important for everybody to be aware of the deep psephological reality, it’s a massive, massive challenge, it would be a quite extraordinary thing in my view if that were to happen [a Conservative majority] – but that doesn’t mean that we’re not fighting for every single vote.”
He added: “I just want everyone to remember, it is so important to support our fantastic candidates up and down the country…
“[On] Thursday we have a crucial series of elections.”
Survey puts Tories ahead
The Tories will be buoyed by the Survation study for ITV’s Good Morning Britain which put the Tory candidate Jill Mortimer on 50 per cent and Labour’s Paul Williams on 33 per cent.
The results were based on 301 people interviewed between April 23-29, a sample size around two thirds smaller than most polls, so it could be significantly less accurate.
In a personal boost to the Prime Minister, though, the analysis also showed that 51 per cent of the Hartlepool electorate viewed him favourably and 28 per cent unfavourably, giving him a net favourability rating of +23.
In contrast, Labour leader Sir Keir Starmer had a net rating of -18.
Mr Johnson was backed as the best Prime Minister by 56 per cent, 37 points ahead of Starmer on 19 per cent, with Liberal Democrat Sir Ed Davey on three per cent.
The sample size for this section was 517, so around half that of most polls so it may also be open to greater inacurracy.
However, the findings, will be a boost to the Tories so close to the by-election.
They also suggest Mr Johnson and his party have not seen their popularity significantly hit among the Hartlepool electorate by the “sleaze” storm at Westminster over his lavish flat refurbishment.
All the other contenders were on single figures, with Thelma Walker, Independent, six per cent, Sam Lee, Independent, also six per cent, Rachel Featherstone, Green Party, three per cent, Andrew Hagon, Liberal Democrats, one per cent, and John Prescott, Reform UK, also one per cent.
Watch: Conservatives and Labour both have reasons to be nervous about May's elections