A good starting point would be to use a savings comparison site. Savvywoman's Top Deals link to Moneyfacts’ savings best buys allows you to do a general savings search and you can enter the regular amount you want to save. However, with the Bank of England base rate so low, savings rates are also generally are very low.
My advice would be to shop around for deals and make sure you review the account annually to check it is still competitive. Make sure you stay within the depositors’ compensation scheme limits (in very general terms £50,000 per person with any one bank or building society – depending on how it is licensed). Consider fixed rates but bear in mind that if the Bank of England raises the base rate you could be stuck in a low fixed rate savings account while rates are rising around you. Check out the terms of any savings deals you are considering, many now offer good rates but only if you also invest in a stocks and shares based investment too.
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