Sir Keir Starmer has defended his leadership of the Labour Party as polls suggest he is struggling to overhaul support for the Conservatives during the coronavirus pandemic.

He acknowledged the party has a “mountain to climb” after the crushing defeat under Jeremy Corbyn in the last general election but insisted it has made “a step in the right direction”.

Early warning signals are ringing among some Labour supporters, with the party not overturning the Tories’ lead despite the UK having one of the highest death tolls from Covid-19 in the world.

Instead opinion polls have put the two parties on similar levels in recent months, after Labour sank to 32% in the 2019 election compared to the Conservatives’ 43%.

After a difficult week for Sir Keir, he insisted Labour’s “priorities are in the right place”.

He cited the party’s campaigning against a Universal Credit cut and dangerous cladding and noted he “started in a very poor place a year or so ago”.

In a pub in Thurrock after a visit to Basildon town centre, Sir Keir told reporters: “We’re now getting to a position where on the polls we’re about even, so that’s a step in the right direction.

“But we’ve got a long way to go between now and 2024 and we’re going to be working hard at this with real determination, every day, every week, every month, every year, into that election in 2024.”

Asked about concerns over his leadership, Sir Keir said: “The vast majority of our party and our movement are behind what we’re doing.”

The latest polls put Labour as having 38% of the vote in Great Britain, compared to the Tories’ 41%.

But with the next general election likely to be years away, Sir Keir faces a more immediate test during the local elections in May.

Last week, he was forced to apologise after falsely denying having previously supported the UK remaining a member of the European Medicines Agency after Brexit.

After accusing Boris Johnson of talking “complete nonsense” during Prime Minister’s Questions, Sir Keir said he had “misheard” Mr Johnson’s charge in retracting his remarks.

Shadow attorney general Lord Falconer also had to apologise for previously having described the Covid-19 pandemic as “a gift that keeps on giving” for lawyers.