The current rates being offered by financial institutions on instant access savings accounts are now so low, if you have any debt whatsoever there is little point in saving as your interest gains are being wiped out by the interest you are paying on your debts.
It was reported recently than many banks standard savings account are offering interest as low as 0.5%. Even in the best buy tables for instant access savings accounts the top rate is 3.15% per year.
As the average credit card interest rate is now above 19% per annum and the average unsecured personal loan has an interest rate of over 10% there is no point in having savings if you have either an outstanding loan or you are carrying even a small balance on your credit card.
Once you have paid off any outstanding debts you can get back to saving and you can be sure you are not costing yourself money.
If you are in the situation where you have no debt except your mortgage then it may be better to overpay your mortgage than have your hard earned cash earning next to nothing in a savings account. At the very least you should move it to a savings account that is earning you the best rate of interest possible
The Best Best Buys has a number of financial product guides that can help you get a better understanding of the options you have available.