Embassies and consulate offices for Germany, Italy, Sweden, Poland and Hungary all reported a surge in interest in the days immediately after the Brexit referendum.
The German embassy in London was getting about 200 calls and emails a day immediately after the vote, a tenfold increase on normal levels, a spokesperson said. The pace has slowed a bit but about 100 people a day are still contacting the embassy.
The Italian embassy in the U.K. said it received about 500 calls after the referendum from people inquiring about Italian citizenship applications.
"We usually get 10 a year," a spokesperson told CNNMoney.
The embassies of Sweeden, Poland and Hungary are also expecting a surge in enquiries.
This surge in applications would definitely put "significant pressure on the system."