The deadline to register to vote in the EU referendum looks set to be extended after David Cameron urged people to continue to sign up.

The Prime Minister said urgent discussions were taking place with the Electoral Commission, which has also called for an extension following a last-minute glitch for those trying to register online.

Mr Cameron told MPs that record demand had caused the system to “overload”, adding that the Government was working with the Electoral Commission to ensure those who registered today and last night were able to vote on 23 June.

He said “legislative options” were being looked at to extend the official deadline.

In a new statement this morning, the Electoral Commission said many people who wanted to register last night would not have been able to as a result of the technical fault, which hit the website at around 10.15pm and was not resolved till after the midnight cut-off point.

The Electoral Commission said: “It is vital that everyone who wants to participate in this historic referendum is able to.

“There was a very significant increase in applications to register to vote yesterday on the Government’s website. However, issues with the government website arose around 10:15pm and were not resolved until after the registration deadline at midnight.

“The Government are looking into exactly what happened.

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“There will be many people who wanted to register to vote last night and were not able to. The registration deadline is set out in legislation and we have said to the Government this morning they should consider options for introducing legislation as soon as possible that would extend the deadline. We would support such a change.”

The leaders of Labour and the Liberal Democrats have both called for the deadline to be extended, after technical problems hit the government website amid what the Cabinet Office called “unprecedented demand”.

Following a publicity blitz on social media, more than half a million people applied to register to vote online yesterday ahead of the midnight deadline.

Neither the Electoral Commission nor the Cabinet Office, which has responsibility for the website, could confirm how many potential voters had been affected by the technical glitch. Government sources said officials were looking into whether it was “practical and legal” to extend the deadline.

Jeremy Corbyn, whose Twitter account was directing people to the website at hourly intervals ahead of last night’s deadline, said the deadline should be extended after receiving reports that the site had crashed.

The Electoral Commission said that 1.65 million had registered to vote since a campaign was launched to encourage sign-ups a month ago, including 226,000 on Monday this week, and 525,000 yesterday.

Liberal Democrat leader Tim Farron said people should be given an extra day to register, calling the Government’s handling of the situation a “shambles”. He also warned it could have a bearing on the outcome of the vote.

“It is a major blow to the ‘In’ campaign and our prospects of staying in Europe,” he said.

“With individual voter registration, and a big campaign to encourage young people to register, many of whom have been trying to do so last minute, this could have major consequences for the result,” he added. “Evidence shows younger people are overwhelmingly pro-European, and if they are disenfranchised it could cost us our place in Europe.

"It could also turn them off democracy for life.”

A Cabinet Office spokesperson said: "We became aware of technical issues on gov.uk/register-to-vote 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."