Such flexibility has long been a feature of the mobile phone market where customers keep their telephone number when they shop around rival providers.

The idea is being discussed to help boost competition in high street banking which is dominated by the "Big Five" banks, Lloyds (>> Lloyds Banking Group PLC), RBS (>> Royal Bank of Scotland Group plc), HSBC (>> HSBC Holdings plc), Barclays (>> Barclays PLC) and Santander (>> Banco Santander, S.A.).

Banks have said account number "portability" would be costly but the idea now has the support of the Financial Conduct Authority (FCA).

"The FCA found that being able to keep bank account details increases consumer confidence in the bank account switching process," it said in a statement.

"A significant number of individual and small business customers would be more likely to switch if they could retain their account details," it said.

Customers can already move accounts to another bank within seven days, though they have to take a new account number.

The new Payment Systems Regulator (PSR), set up by the government to increase competition and innovation in payment systems, will consider the FCA's evidence.

It said the FCA review, as well as emerging findings from the Competition and Markets Authority's investigation into retail banking, will be on the agenda of its new industry forum.

"We will take that into account about what do we really need for the payments system to deliver going forward, and account portability is clearly in the mix there," PSR Managing Director Hannah Nixon told Reuters.

"The question for me is: is that the best way for delivering particular outcomes? I honestly don't know the answer today and that is work the industry needs to do," Nixon said.

UK junior finance minister Andrea Leadsom has been a supporter of account number portability, telling Reuters last month it could be introduced in stages.

"The FCA also found that account number portability could make switching accounts even easier. We expect the new Payment Systems Regulator to consider these findings as part of its wider work programme," Leadsom said in a statement on Thursday.

The FCA said more could be done in the meantime to improve switching, such as targeted marketing campaigns.

"We now expect the banks to deliver these improvements without delay, and we have given the regulators powers to force appropriate action should they fail," Leadsom said.

(Editing by Keith Weir and David Clarke)

By Huw Jones