It would be unusual, check the T&C's to make sure there is no get out clauses ie: if the the interest rates drop by x amount they can reduce what they are paying.
Are you sure it is fixed rate and not an account paying a bonus for a fixed term, which would mean they an reduce the rate but must continue to pay the bonus.
The whole idea of a fixed-rate saver or loan is that the interest rate can't be altered for the duration of the transactipn. I suggest you challenge the bank.
Their letter usually says whether you can take your money out without penalty following such a change. It wouldn't have been a mid-term change to a fixed saver