Done started the BetFred chain – Britain’s biggest independent bookmaker – with his brother Peter in 1967.
CardOne offers current accounts to more than 20,000 people and businesses across Britain. It charges a monthly fee of £12.50 and does not allow its customers to go overdrawn.
The firm has been generating profits of more than £1m on revenues of about £6m. Done said the company was eyeing acquisitions and aiming to begin lending money by the middle of next year.
“We’re looking at a banking licence,” he said.