You can have £5340 cash in an ISA tax free.
No you can't - you can have as much as you want in an ISA tax free, but you can only add up to £5340 in each tax year. The tax year runs from April to March.
But this is irrelevent to the OP at this stage - he does NOT pay tax. Therefore tax free or not, his savings income isn't taxed (Well, it is, but he can claim it back).

My comments were also for the many others involved in the thread. While slightly off the point I'll add some figures: