High street bank TSB is reviewing the 5% rate it pays out to savers on its best-buy Classic Plus account, MoneySavingExpert.com understands.

With the Bank of England base rate – which influences what borrowers pay and savers earn – at 0.25%, and many bank accounts paying a pittance, the TSB Classic Plus* current account is a top pick for savers with £2,000 or less, paying a whopping 5% AER.

However, that could be about to change.

Customers have told us how, as part of internal market research, the bank has been asking them how they would react if they were to see the 5% interest paid out on up to £2,000 cut to as low as 2%. This would leave customers with just £40 a year if they saved the maximum, instead of the £100 they can get now.

Those who took part in the survey were also asked how they would react to being paid a lower 4% on a smaller maximum of £1,000.

One user emailed us an example of the questions being asked: "A lot of the survey was concerned with my opinion of TSB and the account if they reduced the in-credit interest rate from 5% on £2,000 down to 4% on £1,000, which they say they are considering because of the Bank of England base rate drop.

"They also asked if I preferred 3.5% on £1,250, 3% on £1,500, or 2% on £2,000, as these were other rates they were considering."

Another told us how the majority of research questions asked for his opinion on cutting the 5% interest, adding it "looks like this could change anytime soon".

As well as currently getting hefty in-credit interest, you also get 5% cashback on the first £100 spent each month on contactless transactions on your debit card, meaning you can earn up to £5 per month.

TSB is the latest to either cut or review its rates after the Bank of England cut base rate to 0.25% on 4 August. Santander has already announced that the headline interest rate on its flagship 123 Account will be halved to 1.5% from November while Lloyds, Halifax and the Bank of Scotland's rates are all under review.

What does the bank say?

A TSB spokesperson says: "We regularly review rates across our whole product range, and continue to assess the rates we pay our current account customers given changing market conditions. As part of this we also regularly speak to customers and wider consumers."

If the bank does cut rates, we'll let you know and update our Best Bank Accounts guide, which also contains info on all our top picks.