Given the dramatic drop in interest rates recently if you do not have your money in a high interest savings account you will be earning very little interest indeed - some accounts even fall below the Bank of England's base rate of 0.5%.
Even at a higher rate such as 4%, £1,000 of savings will net you £40 interest over a year - yet if you owe a credit card company £1,000 at an interest rate of 20% it will cost you £200 over the course of the same year, so in most cases it would make sense to pay off your credit card debts rather than to save to ensure you are paying out the bare minimum in interest.
Of course this does depend greatly on personal circumstances and spending behaviour - although it could save you money if you do not run up more credit card debts, if you are an irresponsible spender you may just find that £1,000 you paid off vanishes into shopping and social spending.
If you plan to use your savings to pay off credit card debts ensure you also take the opportunity to cut up your cards and remove any temptation of using your spare credit to spend again. It may be worth keeping your empty credit card account open though as this well help your credit score.
Still, it is important to keep some savings as an emergency fund - so that if you lose your job, get sick or your circumstances change you still have a buffer to rely upon. For this reason it is worth making sure that your emergency fund is still earning a decent rate of interest.