MPs demanded extra time for people to register to vote in the EU referendum after "unprecedented demand" caused the website to crash.
David Cameron was among senior figures who urged individuals to sign up before the midnight deadline but dozens were left frustrated.
A last-minute rush to sign up was stalled after the website failed, with Labour leader Jeremy Corbyn and Liberal Democrat leader Tim Farron among those demanding an extension.
Mr Farron said it could be a "major blow" to the prospects of the UK remaining in the EU if young people were denied a say.
The Government issued an online apology to those who experiences issues and said it was "working to resolve them as swiftly as possible".
A live usage site said there were 32,446 people attempting to access the registration website at around 11:20pm on Tuesday.
Dozens of people posted on Twitter, airing their frustrations with the website.
The Electoral Commission - which oversees the running of the referendum - said it was aware of the issue but pointed out that the deadline was set by Parliament in legislation.
Mr Farron said: "This is a shambles the Government has presided over and people must be given an extra day to exercise their democratic right.
"It is also a major blow to the 'In' campaign and our prospects of staying in Europe.
"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 said.
"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.
"Voters must be given an extra day while this mess is sorted out urgently."