The study also found that 17 million claim to have withdrawn money from these accounts over the last year.
Analysis of the top 50 savings accounts found that eight per cent apply penalties for making withdrawals, such as removing interest payments for a month in which a withdrawal was made.
Helen Cook, head of saving as Sainsbury's Finance, said people could benefit from moving savings to an alternative account given the "rising cost of living and economic difficulties".
She added: "If you don't need to access your savings, these accounts can be very attractive, but if you have to take money out the rate of interest you receive can fall substantially."
Recent research by Norwich and Peterborough Building Society found that 57 per cent of Britons plan to spend less this festive period.
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