In the post-banking crisis world, it is perhaps worth starting with the security of this money. You should only deposit £85,000 with any one institution - anything above that amount would not be covered by the Financial Services Compensation Scheme (FSCS) should your bank go bust.
For any joint accounts the sum protected would be twice that amount, so £170,000. Do be careful though, as the sum protected is not per bank but just per "banking licence" - two separate banks such as First Direct and HSBC, for example, could share the same licence.
We all wish for an account that offers a high interest rate and maintains it, but I am afraid that is not how banking works in the UK at the moment. If you want to achieve all of these objectives, you must be prepared to monitor the interest rate you are getting and move the money around.
There are very few accounts that offer 3% plus interest without a fixed term. A few of the smaller building societies such as Melton Mowbray, Kent Reliance and Aldermore offer accounts at this level with 60 to 100-day notice periods and online access.
If you are going to be moving money in and out of these accounts then the key is to look for ones that offer monthly interest, as this will maximise your return.