Isa transfer advise please

My fixed rate 5 year ISA has come to an end now, and the interest rate falls to 0.05%. 
I have a separate Building Society limited issue online access account which has interest 0.5%.
If I transfer the above ISA money to the online access account, does that mean I lose the benefits of the ISA (or are there any?), as I read that you shouldn't take money out of a cash ISA,,
Is there any need to keep the ISAs these days as all savings are tax free now (and I'm a basic rate taxpayer).


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