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LONDON, July 22 (Reuters) - European Union banks should press ahead with Brexit preparations despite Britain’s departure from the bloc having been being postponed to October, the head of the euro zone’s banks resolution board (SRB) said on Monday.

Many lenders plan to deal with whatever Brexit throws at them by relocating staff and activities from London to satisfy licence requirements at new or existing EU hubs.

Lenders had rushed to get ready for the original exit date of March 29, since delayed to Oct. 31.

“It’s not a secret that with the postponement of Brexit, some of the activities banks had scheduled have been slowed down,” Elke Koenig told the European Parliament.

“There is no reason to postpone. Get prepared, be organised.”

The SRB is responsible for ensuring that the more than 100 banking groups of systemic importance in the single currency area could be closed down without taxpayer bailouts or major economic disruption.

Expanding EU hubs with activities hitherto conducted in London could affect mandatory resolution plans.

Asked if any given bank under the SRB’s remit could now be shut down in an orderly way a decade after the financial crisis that triggered taxpayer bailouts, Koenig said: “I would not go so far to say any of the banks I would put a smiley behind and say it’s fully resolvable...

“There is still work to be done for each and every one.”

A bailout fund at the SRB that banks must contribute to has risen to 33 billion euros and on track to reach 60 billion euros by 2023, she said.

Banks must also issue debt that can be written down to help replenish capital burnt through in a crisis.

Much of this debt has been issued under the legal system in Britain, raising questions about its eligibility after Brexit.

The EU should press ahead with building its own capital market so that banks can more easily issue such debt inside the bloc, Koenig said.

Lawmakers asked whether the SRB should force banks to disclose more details on how resolvable they are, as in the United States. Koenig said there should be more transparency over time. (Reporting by Huw Jones; Editing by Kevin Liffey and John Stonestreet)