The European Central Bank said Monday it had reviewed financial institutions' contingency plans for a possible Brexit vote and the "headwinds" it would bring.

British voters go to the polls on June 23 to decide whether to leave the European Union, a decision that would impact major financial centre the City of London.

Daniele Nouy, president of the ECB banking Supervisory Council, said that "we asked some time ago" what plans banks had in case Britain votes to leave the 28-member bloc.

"Obviously the plans are quite different depending on the possible impact or the possible risk that needs to be covered," she told the European Parliament's Committee on Economic and Monetary Affairs.

"We challenge these plans, we make sure they are up to the headwinds that could be generated on the market," Nouy added. 

"But I would say, this is almost business as usual for banks, to be prepared for specific headwinds."

ECB president Mario Draghi said early this month that the monetary institution was ready for "any eventuality" after the British referendum, while pleading for Britain to stay in the EU.

Europe's sole banking supervisory authority, set up within the Frankfurt-based ECB in November 2014, is directly in charge of the supervision of 129 of the region's biggest banks.