On Monday alone, about 226,000 people submitted applications to take part in the June 23 referendum, according to a British government website
That's more than six times the number of people who signed up on one day a week before.
A possible reason for the surge: Tuesday is the last day for people to submit voter registration details in time to take part in the vote.
Younger people make up by far the largest group registering at the last minute, according to the data. Of the 226,000 who registered Monday, more than 148,000 were under 35. That could be significant, because polls suggest young people are more likely to vote to remain in the EU than are older people.
The government website provides live data of the numbers of people currently using the voter registration page; at one point earlier Tuesday more than 14,000 people were online at the same time.
With polls showing the race is too close to call, rhetoric is ramping up.
"It's a roller coaster. ... There's no other way to say it," said Nic Robertson, CNN International diplomatic editor.
British Prime Minister David Cameron made a fresh appeal this week for voters to keep the UK in the EU. A vote to leave would put a bomb under the British economy, Cameron said, accusing "Brexit" campaigners of performing an economic con trick on the public.
"There's a passionate debate taking place in our country, and we should be proud of the fact that this is an enormous exercise in democracy and an enormous exercise in sovereignty, but we must make this decision on the basis of facts and arguments," Cameron told reporters Tuesday.
If Britain votes to leave the EU, Cameron will have to inform other European leaders formally, triggering two years of complex exit negotiations.
If Britain votes to remain, Cameron will have to make a reformed relationship
with the EU work.