Two-thirds of savings accounts offering an introductory bonus rate pay less than 0.25% when the initial deal ends, according to a website.
Moneyfacts found that 68% of the bonus savings accounts on the market will pay less than the Bank of England base rate of 0.25% once the bonus period has expired.
Bonus savings accounts can be handy for savers looking for a guaranteed rate, as returns are fixed for a certain length of time, typically a year, before the bonus rate expires and the rate falls.
But Moneyfacts warned that when the initial bonus rate ends, "the rate could end up paying next to nothing in some cases".
The website found the average rate after a bonus period has expired is just 0.18%.
But its analysis of accounts available to new customers found that Post Office Money, Skipton Building Society, Tesco Bank and West Bromwich Building Society do have accounts paying 0.25% or more after the bonus vanishes.
In 2015, the Financial Conduct Authority (FCA) said many people with cash savings found it difficult to know what rate they were on. It stopped short of banning introductory bonus rates, as they may benefit some customers, but said it did expect providers to improve the way they communicated about interest rate changes and bonus rate periods.
Moneyfacts said that following the FCA's findings, some "teaser rate" deals were removed from the market.
Rachel Springall, a finance expert at Moneyfacts.co.uk, said it would be wise for savers to make a note of when a bonus rate is due to end so they can make plans to switch to a better deal.
When weighing up the best rate to go for, she said it is also important for savers to compare accounts with a bonus with "best buy" deals which do not come with a bonus rate.
Ms Springall continued: "However, the guarantee of a bonus could still attract some savers, particularly those who want easy access to their cash and are wary of more rate cuts to come."