Plenty of ISAs offer highly competitive rates of interest, but often these include a short-term bonus which disappears after the first year. That means savers who aren’t proactive about reviewing their rates, risk their savings earning paltry rates of interest.

But if you discover your ISA could do better elsewhere, remember that not all ISAs accept transfers from existing accounts, so you’ll need to hunt down those which do.

Here, we take a look at some of the best ISAs that allow transfers in….

Top fixed rate ISAs

Some of the most competitive ISAs are fixed rate accounts, which require you to tie up your savings for a set period of time. If you only want to lock up your savings for a year, then Santander’s new fixed rate ISA launched on March 5, pays 3.5% tax-free  AER with a minimum  investment of £2,500 – and accepts transfers in from other ISA providers.

Alternatively Aldermore pays 3.30% on its one-year Fixed Rate ISA, which can be opened with a lower minimum investment of £1,000. Or if you only have £1 to invest, look at Virgin Money’s Cash E-ISA which offers a rate of 3.00% but only until February 24, 2013.

If you can tie up your cash for two years, Santander is top-of-tables again. Its freshly-launched MAJOR ISA pays a fixed 4.00% over that time. And, as an extra twist, if Roy Mallroy wins one of the eligible golf majors before the ISA matures, customers will earn an additional one-off bonus of 0.10% tax-free.

NatWest and Royal Bank of Scotland's Preferential fixed ISAs are also worth considering over a two-year period as they pay a still-generous 3.90% on a minimum investment of £1,000. However, the offer is only available to customers who are transferring an ISA from another provider, and not from another RBS or NatWest ISA.

NatWest and RBS are market-leaders for three-year ISA deals, with their Preferential fixed ISAs paying 4.20% annual interest tax-free on a minimum investment of £1,000. But again, these accounts are only available to those transferring money from ISAs held with other providers.

In the five-year fixed rate ISA stakes, Halifax launched a market-leading deal on March 5 priced at 4.50% for a minimum deposit of £500, which also accepts transfers in.

Remember that if you are transferring your ISA savings, you mustn't withdraw the cash to pay it into a new account - otherwise your savings will lose their tax-free status. Instead, you must request a transfer form from your new provider who should then arrange the switch on your behalf.

Best variable rate ISAs for transfers

If you'd rather not lock into a fixed rate ISA, then there are plenty of competitive variable rate ISAs which still accept transfers in.

Look first at Santander’s new market-leading Direct ISA issue 9 which pays 3.30%, allows transfers in from other ISAs as well as access to your money at any time. It does require a minimum deposit though of £2,500.

Nationwide Building Society's Online ISA Issue 3, also pays a generous 3.10% annual interest tax-free on a minimum investment of £1,000.

However, you must be an existing Nationwide customer to be eligible for this account. The rate includes a hefty 2.10% bonus until the end of September next year.

Alternatively, Principality Building Society's e-ISA Issue 2 account pays 2.80% on a minimum investment of £1. The rate includes a 1% bonus which is payable for the first year.

Remember that as these accounts include bonus rates you will need to move your money again once they disappear to ensure your savings are earning as much interest as possible.

‘Clean rate’ ISAs

If you don’t want the hassle of having to switch your savings every year, you may want to consider a ‘clean rate’ account. These don’t have introductory bonuses, so the rate won’t suddenly plummet after the first year.

Two of the best clean rate ISAs are from Virgin and Marks & Spencer Money. Virgin’s Easy Access E-ISA, for example, pays 2.85% tax-free on a minimum investment of £1 and allows unlimited withdrawals without notice.

The M&S Advantage Cash ISA pays an even higher 3.00% annual interest tax-free on a minimum investment of £100, and again this rate does not include a bonus.

Bear in mind, however, that if you do opt for a clean rate account, there is no guarantee that the rate will remain competitive. In this case, it’s important to still keep an eye on the rate and move your money if better deals become available elsewhere.

Stocks and shares ISAs

If you want to dip your toe in the stock market and are prepared to accept a level of risk with your savings, then you could consider transferring to a stocks and shares ISA.

You can move from a cash account to stocks and shares but not the other way round. Don’t just pick any old equity ISA to invest in – you should seek independent financial advice to ensure you pick the funds and sectors which are most appropriate for your needs and risk profile.

David Jeal, head of product development at online stockbroker Selftrade said: “Transferring a cash ISA is pretty straightforward – just give your current provider instructions to transfer it to your new provider.

"Most will have a simple form for you to fill in. The ‘target time’ for completing a transfer is 15 days and you shouldn’t lose out on any interest during the transfer.”

Please note: Any rates or deals mentioned in this article were available at the time of writing. Click on a highlighted product and apply direct.