You don't pay tax on the interest earned in an Isa but you need to keep an eye on the interest rate which will drop to next to nothing after a year. You can open another ISA in the following year and transfer your existing one to that. I open a new ISA ech year and transfer the existing one. Banks rely on the inertia of savers to keep their money for little interest.
6 years ago I got the amazing ISA deal - 6% for a fixed rate of 4 years. But that was then....These days, we are lucky to get 2.5% and that is with a first year bonus which is then removed.
It's a confusing market as to where you should put your savings, but my first choice is Premium Bonds (you get a chance to win £1m per month), then the best ISA you can get, then a savings account.
I will do as Johnk suggests and just keep moving my ISA each year.