The Government's official advice is not to move banks because of fears of identity fraud. Instead, we are urged to keep an eye on our bank statements and watch for any unusual transactions.
But according to many financial experts, we should have been thinking about switching our bank accounts a long time ago, particularly if we bank with one of four major banks.
Research by consumer champion Which? shows that 61 per cent of us still bank with Barclays, HSBC, Lloyds TSB or NatWest even though they offer only 0.1 per cent interest on many of their current accounts.
In its survey of customer satisfaction, Which? found that seven high street banks scored only two out of five stars - with the Nationwide and the Halifax being the exceptions.
The highest scores went to internet and telephone banks which rated highly. Alliance and Leicester, Cahoot, First Direct, Intelligent Finance, Nationwide, Smile and the Halifax came out as the favourites.
Smile, whose customers were the most satisfied overall, received a Which? award for being the UK's best current account provider in 2007.
So what's stopping you? For most of us it is the hassle of switching direct debits, standing orders, salary payments and so on. But in reality, your new bank does most of the work.
Which? found 75 per cent of people found it easy to switch, with 34 per cent saying it was very easy.
Michelle Slade, personal finance analyst at Moneyfacts, the online financial experts, says: "For a customer with an average credit balance of pound;2,000, switching from an account paying 0.10 per cent to one that offers 6.31, could earn you almost pound;125 extra interest in a year.
"Perhaps this figure is evidence enough that it is worth the hassle."
Michelle says you must do your homework before switching. Use www.moneyfacts.co.uk or www.which.co.uk to find out which account would suit you best.
Once you open your current account, ask your new bank to contact your old bank for a list of direct debits and standing orders. Confirm which payments you want moved.
Then arrange for your salary and other regular monthly payments to be paid into your new account.
This process can take several weeks, so it's worth keeping money in both accounts until the switch is completed.
But some banks offer interest-free overdrafts during this period to help protect against timing discrepancies.