Have a look on the NS&I website.
They have a Direct Saver ISA paying 3.8%, variable, tax free. It looks as if you can access the money any time but always worth checking.
They have a Direct Saver which is accessible paying 3.45% taxable.
They have various fixed term Bonds where your money is locked away for the term. The shortest (1 year) seems to pay slightly more. You could just buy another after a year. They are taxable. Be careful, unless you want to take the interest as income, to go for a Growth Bond, where the income is added to it, rather than paid out to you.
You can open these online and, experience with a relative has shown me that, if you need help they are very helpful on the phone.
You can probably get better rates elsewhere and a Stocks and Shares ISA would probably pay more, with some risk. I have one from a bank that has been rubbish, however.
You would be wise to shop around, but the NS&I figures are a useful baseline to compare with, being very secure, guaranteed by the government.