But in return for the higher interest rate, if a withdrawal is made in any month except July, no interest is earned on the account balance for that month.
Savers can have the monthly interest paid to a nominated current account, without any loss of interest, which is not treated as a withdrawal.
Hetal Parmar, savings manager at A&L, said: "We have guaranteed to keep the rate at least half a percent above the Bank of England base rate until 28 February 2010.
"People who need to regularly access their savings should choose one of our other savings accounts, such as PlusSaver, paying 5.25% gross pa/AER, which allows instant and unlimited access from the linked Premier current account.
"Having two accounts enables you to get the best of both worlds. You can maximise the interest while you build up a bigger nest egg in eSaver, whilst being able to dip into PlusSaver whenever you want."
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