Kevin Mountford, of Moneysupermarket.com, said: “Banks and building societies are keen to attract more retail customers to build up cash reserves. To do this they are penalising existing customers who may not notice, while enticing new customers with top rates.”

A survey reveals that customers are missing out on £870 a year if they stay with the same insurance, savings and mortgage providers.

Julie Harris, of Moneyfacts.com, said: “It is always a good idea to ask your existing lender if they can offer you a better deal.”

New customers of car insurance providers can be offered discounts for buying policies. Incentives from the Post Office, for example, include £50 cashback and Tesco takes £50 off shopping bills.

However, Moneysupermarket.com point out that for current customers the renewal rate for policies can be 100%.

Richard Mason, director of Moneysupermarket.com, said: “Money-savvy motorists will know there are other ways of reducing your motor-insurance premiums, by parking your vehicle in a garage, for example, but the simple action of shopping around on your renewal quote can clearly save hundreds.”