It follows the introduction of the new “Consumer Duty” in July, which requires financial firms to ensure their products and services deliver fair value to their customers and act if they do not.

The FCA said that since this plan was published, it has seen greater availability of higher interest rates in both term limited and easy access accounts. It has also seen moves by some savings providers to align the rates available on accounts currently on sale and those now closed.

But it has asked nine, currently nameless, savings institutions to provide it with their assessments of what value their savings products offer.

The regulator will now analyse the information the banks and building societies have provided. It will publish an update later this autumn, including any steps it might take if it identifies areas of concern.

Mark Hicks, Hargreaves Lansdown head of active savings, said: “The large high street banks have been getting away with not passing on interest rates to their customers for too long – relying too heavily on customer apathy.

“On the face of it, it looks like this could drive change, but it could still be too easy for the high street banks to continue to offer poor rates to the majority of their clients, as their high-paying easy access accounts are often capped at very low amounts.

“So, unless this point gets addressed, whilst it is positive to see the FCA taking the next step in analysing the fair value of banks and building societies savings rates, the danger is it’s unlikely we will see any fundamental change for the majority of customers.”