The FCA said that the first engagement with bank staff could be improved and eligibility criteria was not always identified.
They also found some inconsistency in the way banks asked for identification and verification documents, with some staff unaware of the variety of options.
Five out of the nine banks who provide Basic Bank Accounts (BBAs) were reviewed during the mystery shopping exercise which included both phone and in-branch contact.
The FCA undertook these mystery shops to check whether vulnerable customers in need of a BBA were being correctly offered one.
While bank staff showed understanding of BBAs in an interview situation, this didn't always translate to a seamless customer experience.
Despite being given explicit information during the first enquiry which should prompt a staff member to offer a BBA, staff did not consistently act on this and several banks operated on the principle that BBAs would be offered in the later stages of opening an account.
Frontline staff also failed to identify and support potentially vulnerable customers on several occasions. The FCA found staff did not respond correctly when customers with vulnerable characteristics presented themselves or they incorrectly told a customer they weren't eligible for a BBA with that bank.
Finally, while the FCA noted all banks displayed a range of identification options on their websites, this wasn't consistently applied by frontline staff who only gave common documents like passports and utility bills as options.
Following the mystery shopping exercise, the FCA has encouraged all banks to create a customer journey that's inclusive of vulnerable customers.
They say banks should consider how best to support customers who find themselves excluded from participating in financial services and how they can help to prevent that exclusion from continuing.
In addition, they've asked banks to consider how the current structure of the customer journey in accessing BBAs helps or hinders customers' participation in the scheme.
As a key priority for the FCA is how vulnerable customers are affected by the financial services sector, they will continue to monitor BBAs and how banks offer them to customers.
BBAs allow customers who may otherwise be excluded from accessing a bank account to have access to one with basic features.
These accounts are generally free from fees, they don't require a credit check, they can't have an overdraft facility attached and have specific eligibility criteria.
However, they allow customers to set up direct debits and standing orders, along with providing an account for wages and benefits to be paid into. Money can be deposited without paying fees and can be withdrawn over the counter or at an ATM.
Our full guide to these bank accounts can be found here, including details on how to switch to a BBA and what other alternatives are available.
Basic accounts have long been available in various forms, but they experienced a crisis in 2012 when Co-operative Bank stopped accepting applications from undischarged bankrupts because they were getting too many of them.
This was followed in 2014 by a deal between the Government and nine major banks and building societies to protect the rights of vulnerable customers entitled to a BBA.
A year later, just before all these BBAs were supposed to have been launched, we questioned what progress had been made.
Five years on, Basic Bank Accounts are offered by all major banks and can be found as part of a search to switch current accounts with our free comparison tool - just narrow down the results to show only 'Basic' accounts using the filter.
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