More than 19,000 applications have been made in the first six months of this year alone.
The figure is already significantly higher than the total number received last year.
Richard Tice, co-chairman of campaign group Leave Means Leave, said: “This is evidence that EU citizens think that Britain will be better off because of Brexit and want to be a part of this exciting opportunity.
“The huge economic benefits Brexit can bring is clearly enticing people from the EU to secure British citizenship.”
But critics suggested that the applications were being driven by the fears of European Unionnationals for their post-Brexit future.
Last week Foreign Secretary Boris Johnson told the three million EU citizens living in the UK that they would retain all their rights after Brexit – whatever happens in the negotiations with Brussels.
But his comments risked opening up a fresh split with Prime Minister Theresa May, who has said she will make that guarantee when she has a similar one on the rights of British expats.
Brexit Secretary David Davis is due to update the cabinet on the negotiations on Tuesday, including what has been billed as an “upbeat” assessment of the no deal option.
Despite differences within the Cabinet, Government sources said that they were more united than their EU counterparts.
A row has broken out between the EU’s chief negotiator Michel Barnier and another key official Martin Selmayr, who both report to the European Commission President Jean-Claude Juncker.
Meanwhile Mr Junker publicly disagreed with European Council President Donald Tusk earlier this month over claims of “deadlocked” talks.
A source said that UK ministers may have their disagreements “but at least we don’t have them when standing on the same podium”.
Mrs May secured a significant victory recently when she persuaded EU countries to begin preparations for post-Brexit trade talks with the UK.
Days later she urged EU leaders to publicly guarantee the rights of British expats after Brexit.
In total 19,260 EU nationals applied for Brutish citizenship in the first six months of this year, the Home Office figures show.
In the 12 months before the July 2016 vote to leave the EU, 15,871 EU citizens applied.
In the 12 months after that number was 28,502. The latest figures were provided by the Home Office minister Baroness Williams of Trafford in answer to a question from a fellow peer.
Statistics have also shown that tens of thousands of British citizens have applied for passports from EU countries such as Ireland.
It was recently confirmed that Oscar-winning actor Colin Firth has successfully applied for Italian citizenship.
Lib Dem Brexit spokesman Tom Brake said: “These figures show just how many EU citizens have integrated and want to make Britain their home.
“But instead of valuing their contribution, this government is still using them as bargaining chips.
“The Government should give EU nationals here the right to stay.
“We also need to ensure the Home Office has the resources to process all these applications and not leave families in limbo.”
Last night Lib Dem leader Sir Vince Cable called on Mrs May to act after it emerged that the UK could be forced to wait 35 years to retrieve its investments from the EU’s official bank.
The head of the European Investment Bank Alexander Stubb has said it could take until 2054 for the UK to recover £3billion in payments.
October 30th, 2017: Express