BRUSSELS (REUTERS) - The European Union will move its London-based bank regulator to Paris or Frankfurt following Britain's decision to leave the bloc, while the European Central Bank will insist euro clearing occurs in the euro zone, a senior EU official said on Tuesday.

While the decisions must still be agreed, the choice of France and Germany for the European Banking Authority would dash Italy's hopes of hosting the regulator in Milan.

Upholding ECB policy on clearing houses, a policy Britain has already successfully challenged at the European Union's second-highest court, could diminish the influence of London's financial sector.

"The multi-currency union narrative is over. That's why you will see the European Banking Authority going either to Paris or to Frankfurt," the official said.

The EBA, which writes and coordinates banking rules across the bloc, is expected to be relocated soon, two EU officials told Reuters immediately after the British referendum result.

"That's why you can be sure the ECB will install its location policy now. Not tomorrow, not in two weeks, but this is going to happen over the next two years," the official said, referring to a policy that euro clearing houses should be based in the single currency area.

Britain last year successfully challenged ECB policy saying that euro clearing houses should be in the euro zone.

That victory, at the European Court of Justice's General Court in Luxembourg, avoided Britain being forced to move large parts of the London Stock Exchange's LCH.Clearnet euro-denominated operations to continental Europe.

The ECB had argued that having clearing houses inside the euro zone would make it easier to intervene if they got into trouble.

However, outside the European Union, London would have little hope of keeping the activities.

Clearing houses stand between the two sides of stock and bond trades, ensuring smooth completion of transactions even if one side goes bust.