By Ines Kagubare

BRUSSELS (Reuters) - Belgium is receiving hundreds of requests from British nationals keen to get Belgian citizenship following the decision of British voters in last Thursday's referendum to back leaving the European Union, officials said.

Nearly 24,000 British citizens live in Belgium, about a third of them in the capital Brussels, where many work for the EU institutions and for NATO which are based in the city.

Dominique Dufourny, the mayor of the Ixelles borough of Brussels, said around 40 people had come to get the necessary documents in the last few days.

"It doesn't stop. Some have been queuing up for information since 7.30 this morning," she said.

Other Brussels boroughs speak of similar numbers of British citizens requesting information about becoming Belgians.

About 50 requests have arrived on local government desks in the affluent suburbs of Uccle and Woluwe Saint Lambert.

"Normally we rarely have anybody requesting information about citizenship," a spokeswoman for Woluwe Saint Lambert said. "Since Friday there has been an explosion."

People are eligible for Belgian citizenship if they have lived and worked in the country for more than five years and can show a basic command of one of the country's three official languages: Dutch, French or German.

Those who have not worked need to have lived in Belgium for more than 10 years but also need to prove that they have integrated into Belgian society to some extent.

About 1.3 million Britons live in other EU member states, while some three million EU citizens currently live in Britain.

British Prime Minister David Cameron, who plans to step down in the autumn after campaigning in the referendum for a vote to stay in the EU, has said there will be no change in their status for the time being. The Brexit negotiations are expected to last several years.

Dennis Landsbert-Noon, a British national based in Tervuren, in the commuter belt outside Brussels, said he was gathering documents needed to apply for Belgian citizenship for himself, his wife and their four children.

"I believe that the consequences of Brexit on Britain will be catastrophic in both the short and long term and I do not want to condemn my children to belong solely to a nation that is on the road to ruin," he told Reuters.

"I've heard from a lot of people who say they are doing the same thing as well."

The Tervuren district said it had received some 40 requests since Friday.

(Reporting by Ines Kagubare, writing by Robert-Jan Bartunek; editing by Philip Blenkinsop and Gareth Jones)