Thats why many people locked into fixed rate accounts from the middle of 2008, and again this Spring. Many banks/building socs. now launch new accounts to attract new money and once they have acheived their targets start to ramp down the interest rate.Examples I can think of include Scottish Widows (was 3.35% inc bonus , now 2.1% inc), IF (Raised from 1.1% to 2.85% to attract cash , now back to 2.49%) and EGG, who are forever launching new attractive rates for new money then let the old accounts slip back.
However, if you are sure your interest rate has been cut then it is a variable rate account - few of these will have any penallty clauses attached and you should be able to transfer to a better paying account without any issues.