Performance based on set criteria should be measured every three months from April 2018, and published on a bank's website within six weeks of the end of the quarter, the FCA said.
First publication is expected in mid-August 2018, with issues such as the pace of setting up new accounts and how banks respond to reports of lost or stolen cards being evaluated.
The government wants to increase competition in banking, a sector long dominated by the "Big Four" lenders, HSBC, Lloyds, Barclays and Royal Bank of Scotland, but is now seeing many new entrants or "challengers".
Regulators have also made it easier to switch banks, but number of customers making the change is still low, and total market share of challengers remains modest.
A review by the Competition and Markets Authority in 2016 ordered more changes and on Tuesday the FCA outlined how it would apply one of them, known as objective service metrics.
Banks already provide data on services, but rarely in a consistent way, the FCA said.
"Customers tell us they think 'all banks are the same' and so they are discouraged from looking for current accounts offering better performance," said Christopher Woolard, the FCA's executive director for strategy and competition.
"These proposals represent a step forward, making it easier for consumers to judge whether their bank is offering good service and for firms to see if they are competing effectively against other providers."
Under the proposals put out to public consultation, banks that offer personal and business current accounts would have to say how long it takes to open an account, and how long it takes to replace a lost, stolen or stopped debit card.
They would also have to show how long it takes to give someone access to the account under a power of attorney, and the number and type of major operational or security incidents - a growing concern as the number of cyber attacks multiply.
The data would also be available for online services that compare different banks.
The new requirements would apply to lenders with more than 70.000 personal or 15,000 business accounts "per brand". The data would not include details on fraud or individual staff members.
Smaller banks and credit unions would be free to apply the new rules, if they want to, and the FCA will monitor customers' attitudes and behaviour to assess the impact of the changes.
(Reporting by Huw Jones)
By Huw Jones