Prime Minister David Cameron's government, elected last month, set this target to challenge the so-called "Big Four" banks, HSBC, Barclays, Lloyds and Royal Bank of Scotland, which dominate the market for retail customer accounts.
"We expect that to be achieved. We expect that to be exceeded," Martin Wheatley, chief executive of the Financial Conduct Authority, told a financial conference.
In the past two years, 14 new banks have been authorised and a further 20 are now in the early stages of seeking authorisation, Wheatley said.
But Wheatley also said introducing new banks to the market was not purely a "numbers game" and that having a very large number of banks, such as the 700 banks operating in Italy, was probably not a good thing for customers.
Adding some new entrants, increasing innovation in banking services, and being a "referee" to ensure customers are put first, were the FCA's key to improving competition, he said.
The watchdog has also given advice to about 100 so-called fintech firms, many of them based in London's Shoreditch district, known for being a tech start-up hub.
Some of these businesses want to offer services in cyber currencies or make it easier for people to open a bank account when they move to another country, Wheatley said.
(Reporting by Huw Jones. Editing by Jane Merriman)
