Matt Hancock, the minister for Cabinet Office and Paymaster General, said Wednesday that legislation would be passed to extend the deadline to register until midnight Thursday local time -- two days past the original deadline.
"We think it is right to extend to midnight tomorrow to allow people who have not yet registered time to get the message that registration is still open and get themselves registered," Hancock said.
An unprecedented surge of 525,000 people registered Tuesday, trying to submit their details ahead of the cutoff that day for the June 23 referendum on whether to leave the European Union.
That was more than seven times the number who had applied the previous Tuesday.
The Electoral Commission said in a statement Wednesday that "many people" would have missed out after issues started arising at 10.15 p.m. Tuesday -- when more than 50,000 were trying to register on the site at the same time.
"There will be many people who wanted to register to vote last night and were not able to," the statement said.
Some people who had found themselves unable to register took to Twitter to vent their frustrations, with the hashtag #ExtendTheDeadline circulating as news of the technical failure spread.
British Prime Minister David Cameron told Parliament earlier Wednesday that he was urging people to register to vote using the website as he worked on a legislative solution to extend the deadline.
Other politicians urge extension
Politicians on both sides of the debate, as well as the Electoral Commission, said they supported an extension.
Opposition leader Jeremy Corbyn of the Labour Party tweeted that if the site had crashed, then the deadline "has to be extended."
The rival "Vote Leave" and "Vote Remain" campaigns have been neck and neck, with pundits saying the race is too close to call.
But those in the latter camp are likely to take encouragement from the last-day surge in registrations, which came disproportionately from younger voters who are widely seen as more in favor of remaining in the EU.
Government figures on voter registration
showed that the largest group applying Tuesday (170,000) were ages 25 to 34, followed by those under 25 (132,000).
The spike in advance of the cutoff began Monday when 226,000 people applied to vote.
Campaign ramps up
Cameron made a fresh appeal to voters this week, saying that a vote to leave the EU would put a bomb under the British economy, and accusing "Brexit" campaigners of misleading the public.
He continued his appeal during parliamentary questions Wednesday, saying: "I don't accept for one minute that in any way supporting Britain being a member of a reformed European Union is doing our country down."
He went on: "I think if you love your country, you want it to be strong in the world. If you love your country, you want opportunities for your young people."
If Britain votes to leave the EU, the country will engage in two years of complex exit negotiations.
If Britain votes to remain, Cameron will have to make a reformed relationship
with the EU work.