Financial rules in Britain are written by the European Union, which the UK is due to leave in March.

"There may be a reasonable case that a simpler -- simpler not weaker -- regime for small firms would advance both our safety and soundness and competition objectives," Deputy Governor Sam Woods said in a speech.

"It is impossible to know at this stage, but under some Brexit outcomes we might have room to revisit this question for small domestic firms," said Woods, who heads banking supervision.

He said the central bank was taking a close interest in "radical steps" being taken by U.S. and Swiss regulators to make banking rules simpler for small lenders, although he said the BoE's focus remained ensuring banking was safe and sound, before fostering competition.

He said Britain's central bank had authorised 17 new lenders in the past five years but none had become a major bank, which he said could be due to the reluctance of customers to switch accounts, known as "stickiness".

Barclays, Lloyds, RBS, HSBC, known as the "Big Four", dominate retail banking in Britain.

Woods said it was not yet clear whether "Open Banking" reforms to help payments firms challenge banks would become a gateway for bigger change.

Some British lawmakers have said Britain's financial regulators should have a formal objective to keep London's banking and insurance sectors competitive after Brexit.

"I have a number of reservations about this idea," Woods said, adding that the Financial Conduct Authority and the Competition and Markets Authority already had competition as a primary objective

Adding such an objective to the BoE's remit would risk overlap and could dilute its focus, the deputy governor said.

"The same logic applies to a competitiveness objective, which surprisingly often gets confused with our competition mandate," Woods said.

Britain's now defunct Financial Services Authority had a requirement to pay heed to competitiveness, which led to criticism that "lite touch" regulation fomented the 2007-09 financial crisis.

(Reporting by Huw Jones; Editing by Edmund Blair)