Update: The Government has extended the EU referendum registration deadline to midnight on Thursday

Jeremy Corbyn and Yvette Cooper have led calls for the extension of the deadline to vote in the EU referendum after the Government website crashed as demand soared hours before the deadline.

The Labour leader, who had been urging people to add their name to the electoral roll, last night demanded extra time after a series of would-be voters were rebuffed by an error message in the final hours before the midnight cut-off.

Cooper complained about the “computer says no” response after thousands of people logging on were met with the words “504 Gateway Time-out”. Public demand to register to vote appears to have risen sharply amid a series of high-profile television programmes, with David Cameron and Nigel Farage taking questions in separate sessions on ITV last night and Hilary Benn receiving a grilling from the BBC’s Andrew Neil on Monday.

Last night Corbyn, who had earlier issued a series of reminders counting down the deadline to register to vote, wrote on Twitter: “I’m told https://www.gov.uk/register-to-vote … site has crashed so people can’t register to vote for # EUreferendum. If so, deadline has to be extended.”

Cooper, the former leadership candidate, said: “If this is right, deadline must be extended. People can’t be denied right to vote because computer says no.”

The site appeared to be working again by Wednesday morning although it was unclear whether those people who had been turned away yesterday would receive another opportunity to vote.

A Cabinet Office spokesman told the BBC: “We became aware of technical issues on [the registration website] late on Tuesday night due to unprecedented demand.

“Some people did manage to get through and their applications were processed. We tried to resolve the situation as quickly as was possible and to resolve cases where people tried to register but were not able to.”

The former Labour MP Tom Harris, who is campaigning for Brexit, wrote on Twitter: “If you waited until 11 o’clock last night to get your arse in gear to register to vote, I’m guessing you’re not that bothered either way.”

By 1.30pm more than 64,000 people had signed a 38 Degrees petition calling for the voter registration deadline to be extended.

Gloria De Piero, shadow Minister for Voter Registration, said: “We need the Government to act to give a 24 hour extension of both the voter registration and postal vote deadlines, so that anyone who has registered to vote today will be able to have their say in the decision of a lifetime.

“We are making an offer to the Government today to support any legislative changes necessary in the Commons and the Lords, to ensure democracy isn’t hijacked just because the computer says no.”