Is it a cash ISA? You can easily get fixed rate ISAs paying at least 5% interest at the moment.
If you move the money, make sure you 'transfer' it between ISAs - don't withdraw the money as it will lose its ISA status. Maybe split the £50k into 2 or 3 fixed rate ISAs with different durations. They'll mature at different times and that can cushion you from changes in interest rates.
How much is the cushion in your current account? Does that account pay interest? You might find an easy access savings account that pays more. See if your existing bank has one, as it's then easy to move the money between savings/current account if you need to spend it.
If you haven't used this year's ISA allowance, you could put some of the £10k in an easy access ISA so that it's accessible. Some have limited access (eg up to 4 withdrawals year) and have a higher rate than an easy access version.
Building societies that offer consistently good rates include:
Coventry Building Society
Leeds Building Society
Kent Reliance
If you're generally reluctant to keep on top of moving savings, I'd recommend a fixed rate ISA with one of the above because when the account matures they will automatically reinvest the money in an account with a similar duration, unless you give them instructions otherwise. As their interest rates are consistently good, you'll safely be getting a decent rate in the new account, rather than languishing year after year at a poor rate offered by many other institutions.