Check www.moneysupermarket.com for the best savings accounts. Also Martin Lewis' www.moneysavingsexpert.com gives you the low-down on the best savings accounts.
You could try the account from Lloyds which is a regular saver...ie you need to deposit each month at least £25 but you can have unlimited withdrawals. Only paying about 2.55% though. Unfortunately the accounts with the best interest rates have conditions where you can't touch your money or you will be penalised.