Banks and building societies are cutting the rates on savings accounts, causing misery for millions of savers.

In October alone, 18 firms slashed the rates on more than 100 accounts, according to SavingsChampion.co.uk. So far in November there have been another 13 rate cut announcements.

For example, Tesco Bank's one-year bond now pays 1.60 per cent, down from 1.75 per cent. Rates on the two, three, four and five year deals have fallen by similar amounts.

HSBC, Nationwide and Newcastle building society are just some of the other high-street names to have taken the axe to savings rates.

Inflation has fallen to 1.2 per cent, its lowest rate in five years, but even so a basic-rate taxpayer at 20 per cent needs to find a savings account that pays at least 1.5 per cent a year. A higher-rate taxpayer at 40 per cent needs to earn interest of at least 1.90 per cent. Sylvia Waycot, editor at Moneyfacts.co.uk, says: "The savings market is in a dire state. Five years ago, savers could get 3.35 per cent in a no-notice account, but today they would need to invest for a staggering seven years to get 3.50 per cent. What savers want is the return of real competition in the savings market and some realistic deals on offer."

Some banks and building societies are, however, bucking the downward rate trend. BM Savings recently launched new issues of its easy access Online Extra and Isa Extra accounts, paying 1.6 per cent on balances over £1,000, a rise from the previous versions paying 1.35 per cent and 1.55 per cent - but after 12 months it falls to 0.5 per cent.

If you have savings of at least £10,000, the Family Building Society has devised an innovative new account, which is in many ways similar to Premium Bonds from NS&I. Holders of the so-called Windfall Bond are entered into a monthly prize draw. There are ten tax-free prizes of £1,000, two of £10,000 and one of £50,000 every month and a one in 64 chance of scooping a prize.

The main difference to premium bonds is that the account also pays an interest rate of 0.50 per cent gross. The rate is guaranteed to match the Bank of England base rate, though this guarantee is reviewed annually. The rate is obviously low, but if you are happy to take a gamble you could win a big prize.

Savers are advised to snap up any good deals as soon as possible as banks and building societies are quick to withdraw best-buy accounts. National Counties building society, for example, recently pulled a competitive fixed account after just three days. Yorkshire building society and Secure Trust Bank have also recently launched top payers only to pull them off the market after a few days due to the high level of demand. Susan Hannums, director of SavingsChampion.co.uk, says: "These are desperate times. Never have we known it so tough for savers. It's clear there is appetite out there, as savers are reacting fast to changes in the market, but we need more competition and better rates to satisfy the clear need of savers to better their returns."

The highest rates are available on fixed-rate bonds, but you have to be prepared to lock your money away for the term of the bond. Remember, too, that if interest rates rise over the term, you could end up with a poor deal.

Coventry building society pays 2.6 per cent in its Fixed Rate Isa until the end of November 2018 on a minimum deposit of £1. Or, you can earn 2.5 per cent with Skipton building society's Online 5 Year Fixed Rate Isa on a minimum balance of £500. For instant access, NS&I and Skipton building society both pay 1.50 per cent on a minimum balance of £1.

Other best-buy accounts include the Saga Telephone Saver at 1.5 per cent, while The Post Office Online Saver, the AA Internet Extra and Coventry building society's PostSave all pay 1.4 per cent - but be prepared to move again when bonuses run out.