The number of these accounts offering savers a bonus has fallen back sharply since the Government launched a scheme to help borrowers last August, Moneyfacts found.
At the start of August 2012, 73 easy access accounts paid a bonus and the highest rate on offer was 2.7%.
Since then, the choice of bonus-paying accounts has plummeted to 32, with the highest bonus rate on offer almost half of what it was nine months ago, at 1.45%.
The Government's Funding for Lending Scheme was launched last August to give lenders access to cheap finance, but analysts have said that this has made them less reliant on attracting borrowers' deposits.
Savers were already struggling to find any deals to give them decent returns on their cash pots, with the bank rate being held at a record 0.5% low.
There has been recent debate about the benefits to consumers of introductory "teaser" rates, which are used to tempt new customers but often drop sharply when the introductory bonus period comes to an end.
Sylvia Waycot, editor of Moneyfacts.co.uk, said the number of easy access accounts offering an introductory bonus is "on the verge of disappearing".
She said: "Bonuses have received mixed reviews, some people love them, others loathe them because of their temporary nature. However, anything that gives you more interest, even if only for a short time is better than nothing at all."