More than a third of deposit accounts aimed at ordinary savers pay returns of 1 per cent or less, after banks and building societies cut savings rates over the new year.

With the Bank of England's Monetary Policy Committee expected to cut official interest rates by at least 0.5 per cent on Thursday, further dramatic reductions are expected.

Michelle Slade, of Moneyfacts.co.uk, the financial website, said: “We have been recording savings rates since 1988 and, if base rate is cut further this week as predicted, we are likely to see the average rate drop to the lowest level ever seen.”

Nearly all banks and building societies have implemented cuts, leaving about 38 per cent of savings accounts for deposits of £5,000 paying interest of 1 per cent or less, Moneyfacts said. This compares with only four accounts, or 1 per cent of the market, at this time last year.

The plight faced by savers prompted the Conservatives to promise to abolish tax on savings for basic rate taxpayers. The Prime Minister has also hinted at help for savers as the interest on some popular accounts has plummeted.

The interest paid by some British banks and building societies cannot fall much further. Savers with £5,000 or less in Alliance & Leicester's instant access account will receive 0.1 per cent per year, as will those in Halifax's Liquid Gold and Abbey's Flexible Passbook Saver accounts.

The British Bankers' Association, the savings industry trade body, has dismissed speculation that returns on such low-paying accounts could turn negative as the base rate continues to fall, meaning that savers would have to pay banks to hold their money.

Rates are expected to keep tumbling, so savers are being urged to grab the best deals while they can.

Yesterday, Close Brothers opened an account fixed at 5 per cent for two years. It requires a minimum deposit of £10,000 and the rate is guaranteed only on applications received before close of business next Tuesday. ICICI, the Indian bank, and Anglo Irish Bank have one-year fixed-rate bonds of 5.1 per cent and 5 per cent respectively. Those looking for an instant access account can get 4.55 per cent from Anglo Irish.

Most banks and building societies that have cut rates in the past week have opted to pass on up to the full percentage point reduction in the Bank of England base rate, or more. The same institutions have been less willing to reduce rates for borrowers.

Research from Moneyfacts found that almost three quarters of lenders have failed to pass on the last base-rate cut to borrowers on variable rate deals. Mortgage experts believe that even fewer banks and building societies will pass on this week's expected cut in the cost of borrowing.

There has also been a sharp increase in the number of mortgage deals that require a 40 per cent deposit - up to 341 from 24 last year. Meanwhile, the number of home loans for borrowers with a 5 per cent deposit fell from 1,023 to 11 in the same period.

Melanie Bien, of Savills Private Finance, the broker, said: “The situation will not improve until house prices begin to show signs of stabilising.”