Cash ISA rates change all the time – last year's best buys may pay next to nothing now because ISAs often include an introductory bonus for the first 12 months. By transferring into another ISA – on top of using your current year's ISA allowance – you can ride the wave of high interest rates.
First of all check how much interest your old ISAs are paying and whether there are any penalties for transferring money out. Most don't have penalties but some require notice periods.
Never withdraw money from a cash ISA because you'll immediately lose all the tax benefits. Find a new provider and open an account, then fill out a transfer form with your new account details and the new provider will move the money over for you. It can take up to 30 days. Do not close your old ISA!
What else do you need to know?
You can transfer a cash ISA into a stocks and shares ISA, but not the other way round. A stocks and shares ISA can only be transferred to another stocks and shares ISA. If you want to move your current year's ISAs to another provider, they must be moved whole, but old ISAs from past years can be split between different providers. The HMRC website also has some information on transferring ISAs.
Unfortunately not all ISAs allow transfers in, especially the top paying ones. The top rate, instant access accounts that allow transfers at the moment include Alliance & Leicester or its parent Santander whose online direct ISAs pay 2.75% AER if you have at least £9,000 to invest (2% if it's less than £9,000). This includes a 2.25% bonus in the first year which means the rate will drop to 0.5% in a year's time – so make a note to ditch this ISA then.
If you're a Nationwide current account customer, you can also get 2.75% with its e-ISA which includes a 1% bonus. The Halifax has an ISA that pays 2.60% without a bonus (this is a limited offer and may be withdrawn at any time).
The consumer group Which? has a cash ISA finder that calculates 12 months' gross interest for you based on how much you would like to transfer in and/or deposit in new money (this can be zero).
Check the best buy tables in the newspapers for the best rates, or search online at moneysupermarket.com or moneynet.co.uk. You will need to decide whether you want instant access or are happy to tie up your money for longer (which pays higher interest, but remember, Bank of England rates will go up at some point so you don't want to lock up your money for a long period and find that you could get a much better deal elsewhere).
Check if there are any strings attached: for example Santander has an ISA paying 5.5% but you have to put an equal amount of money into another Santander account.
So to sum up, in the same tax year you can subscribe to a new cash ISA (and/or stocks and shares ISA) and also transfer money from old ISAs to a new provider. If you're unhappy with the interest after opening a new cash ISA, you can transfer all the money to another bank or building society in the same tax year.