The Financial Services Compensation Scheme (FSCS) protects individual savers up to £85,000 for each savings institution. It therefore makes good sense to divide money on deposit between several accounts with different organisations, keeping each account below this limit.
Crucially, however, the compensation limit is per person, per authorised institution. Therefore you need to be careful that you do not hold more than one account under the same banking brand. It is not always obvious which organisations are linked via the same parent company, but you can check out a list at the Financial Conduct Authority's website at fca.org.uk.
Certain savings institutions are not covered by the FSCS. Again, there is a list available at fca.org.uk.
If you have a large amount of savings it may not be practical to hold many different accounts, so it's worth considering National Savings & Investments (NS&I), which is backed by HM Treasury so is very safe. Sometimes securing capital is more important than the interest rate gained.