MILAN (Reuters) - The European Union will start disintegrating after Italians pick the anti-establishment 5-Star Movement candidate as mayor of Rome on June 19 and Britons vote to leave the EU four days later, the leader of the UK Independence Party was quoted as saying.

UKIP's Nigel Farage told Italy's Corriere della Sera in an interview published on Saturday that British Prime Minister David Cameron should resign even if the 'Remain' camp won by a narrow margin in a June 23 referendum on EU membership.

Bookmakers still predict Britons will vote to stay in the EU, while opinion polls have see-sawed - though one on Friday gave a 10 percentage point lead to the 'Leave' side, for which Farage is a prominent campaigner.

"We can't lose this referendum ... there will be a Big Bang of British politics: nothing will remain the same," Farage said. He said he would "destroy the old EU", together with 5-Star leader Beppe Grillo.

"On June 19 the 5-Star movement elects the mayor of the capital and changes Italy. On June 23 Britain leaves the EU and changes Europe. We will trigger a domino effect. After us, other northern European countries will leave, starting with Denmark," he said. "The EU is about to collapse, disintegrating in several pieces."

Municipal elections in Italy last Sunday put 5-Star candidate Virginia Raggi, 37, in the lead to become mayor of Rome ahead of the candidate from Prime Minister Matteo Renzi's center-left Democratic Party (PD). The race will be decided by a run-off vote on June 19.

(Reporting by Valentina Za; Editing by Mark Trevelyan)