A few accounts offer no interest at all
The rate of interest paid on instant access accounts from banks and building societies hit a five-year low in December at an average of just 0.81%.
The figures, from the Bank of England, also show that interest on notice accounts slumped to the lowest level on record at an average 0.82%.
The rates tumbled as the Bank slashed its Bank Rate to stave off recession.
The return on cash ISAs fell to 3.02% and dropped to 2.09% on fixed-rate bonds - both also record lows.
"The figures are no great surprise," said Michelle Slade of Moneyfacts.
"Rates have been coming down quite dramatically in the last four months.
"This proves that savers are being penalised at the moment and are struggling to find accounts that pay good returns," she said.
In April last year, the Bank Rate stood at 5%. Last spring, instant access rates averaged 2.19%, notice accounts averaged 2.99%, cash ISAs had an average rate of 4.56% and fixed-rate bonds averaged a return of 5.32%.
However, since October the rate has been cut in four successive months as the authorities have tried to stop the contraction in the economy.
As a result, savings rates have come down sharply, and the rates are likely to fall even further.
The Bank of England's data does not yet reflect any reductions triggered by its one and half percentage point cut in December, nor last week's half a percentage point cut, which took the Bank Rate down to just 1.5%.
That means the official cost of borrowing is now at its lowest level since the Bank of England was founded in 1694.
According to Moneyfacts, 60 instant access accounts - 17% of the total - pay just 0.3% or less on sums up to £5,000.
Of those, there are three banks or building societies that pay nothing at all on some of their accounts, one that pays 0.001% and six that pay just 0.05%.