He stressed that given Britain’s fraught public finances, Labour would not support a policy of axing university tuition fees.

“We are likely to move on from that commitment, because we do find ourselves in a different financial situation,” he told BBC Radio 4’s Today programme.

He added: "We are looking at options for how we fund these fees. The current system is unfair, it doesn't really work for students, doesn't work for universities."

He said the party would, in the coming weeks, "set out a fairer solution".

He added that he did not "want that to be read as us accepting for a moment that the current system is fair or that it is working".

But the National Union of Students criticised Sir Keir’s move as “truly disappointing”.

A spokesperson stressed: “The Labour Party needs a clear vision that young people and students will turn up for, and cannot take their votes for granted.

“Students and young people are clear about what we want to see in society: a fair and well funded education, where everyone can afford to study across their lifetime; living wages for all and the vision and innovation to respond to the great challenges of our lifetimes.”

The statement added: “The current system is broken, prioritising money over student welfare and education.

“A failure to invest in education is a failure to invest in future generations and in a prosperous and fair society.”

Sir Keir made the pledge to scrap tuition fees during the 2020 Labour leadership election.

In a New Year’s speech, however, he indicated that the pledge would be kept under review.

Reneging on the promise threatens to spark a backlash among students and in the Labour Party.

Nick Clegg’s Liberal Democrats pledged before the 2010 General Election to the National Union of Students not to raise tuition fees.

But after they agreed a Coalition government with the Tories, they abandoned this stance and the cap on the uni levies was lifted to around £9,000.

Political experts say this broken promise was one of the key reasons why the Lib-Dems lost dozens of seats at the 2015 election.

Sir Keir’s comments on tuition fees, just days before the May local elections on Thursday, could impact on the results.

Labour is seeking to focus on the Government’s record on the cost-of-living crisis, fighting crime, the NHS and the housing shortages, as well as local issues.

Sir Keir also argued that Labour's controversial election advertising campaign has "held the government to account for thirteen years of failure".

Speaking on BBC Breakfast, he added: "I will be measuring progress from 2019 when we had a very bad election result, to the next general election which will be next year, to ensure we can take the Labour party from a failure in 2019 back into government," he said.

But the Labour leader has come under fire for jettisoning a number of pledges he made during the party’s leadership campaign after Jeremy Corbyn stood down.

The Tories have sought to portray him as a “flip-flopping” party leader.

Sir Keir was also asked about how Labour would tackle NHS strikes.

He said, "I don't want to see the strike" but refused to confirm whether Labour would give nurses a pay rise in line with inflation, saying that he didn't want to "go into figures" live on air.

He did promise to double the number of doctors and nurses coming into the NHS.