While you may benefit from using certain types of current account to store your savings, say one that offers cash back when you maintain a high balance, the chances are that you are going to be better off by keeping them in a specifically designed savings account or ISA.
This is because the interest rates that you will enjoy on dedicated savings accounts and ISAs will be much higher.
With ISAs in particular, you can earn interest that is tax free, making them particularly worthy investment. Bear in mind though that you can only deposit a certain amount into an ISA each year – currently £15,240.