The industry-wide protocol, signed in March 2015, requires banks to investigate alternative arrangements before closing the last bank in town.
Those options included free-to-use cash machines, banks on wheels and the use of local Post Office branches.
The review is expected to report by the end of the year.
It will led by Professor Russel Griggs, who previously reviewed the major banks' lending code.
"It is vital that the protocol meets its aim of minimising the impact of bank branch closures on customers and local communities," he said.
"This review will not only be looking at how the processes behind the protocol are working in practice, but also crucially the outcomes that they are delivering."
Before the protocol was signed there was a voluntary agreement to assist vulnerable customers when towns and villages become bank-free.
Banks should now consider the proximity of alternative branches as part of a 12-week consultation before a closure. Proximity can be very different, depending on the mobility of customers, ranging from young car drivers to older people reliant on public transport, so the age profile of the branch's customers will be part of the review.
Under the current agreement, signed by banks, the government and consumer groups, there is no punishment if banks fail to provide alternatives when the last branch closes.
The Campaign for Community Banking Services (CCBS) says many hundreds of communities in the UK have lost all their banks.
Derek French, from the campaign, said: "In practice the protocol, and the necessary published impact statements, are proving to be of little value to communities suffering branch closures as they deal only with post-closure provision.
"At the moment many communities see it as a box ticking exercise rather than a serious attempt to put in place reliable sustainable alternatives to branches for those that need them."
An independent review is to be carried out into an agreement aimed at protecting remaining bank branches in towns and villages.