She criticised the "oligopoly" of established banks, which she said effectively owned the current system, and played down the impact of reforms to current account-switching that came into force last month.
Ms Gadhia told the British Bankers' Association annual conference in London: "My view is that the big banks compete for the share of profit in the current system.
"Real competition means giving customers a better deal.
"It is hard to give customers a better deal as a challenger bank if you cannot break out of the current system."
Virgin, which bought Northern Rock from the Government in 2011, will launch current accounts next year.
Fellow Edinburgh-headquartered challenger Tesco Bank also intends to launch current accounts, entering a market currently dominated by Royal Bank of Scotland, Lloyds Banking Group, HSBC and Barclays.
Under new rules a customer's current account must be switched within seven days.
Ms Gadhia wants further changes, such as allowing customers to retain account numbers when changing providers and described the switching system as "old-fashioned".
Antonio Simoes, chief executive for HSBC in the UK said making account switching even faster was "politically the right thing to do" but added: "I am not sure it is the best thing for customers."
He warned that it could cost the industry billions of pounds.
Mr Simoes said around 5000 customers had been switching current account providers every day since the new rules came in.
Lloyds chairman Sir Win Bischoff told the conference that there must be a halt to "tinkering" with regulation.
"There have been so many things that have been done," he said. "Let's give them a chance to work rather than to have the uncertainty of ever more regulation."
Santander UK chairman Baron Burns of Pitshanger added: "There had to be very significant change in regulation. We hare hopeful we are getting to the end of the road on that."
Sir Win also warned that the prospect of the UK leaving the European Union was the biggest threat he saw to financial services
He said that as New York had the might of the US behind it, the UK required the "hinterland" of the rest of Europe to ensure it was a successful financial services centre.