How do I move an ISA without losing it?

Take cash out of an ISA to move it and it stops being ISA money. Putting it back uses up this year's allowance, and if you have already used the allowance you simply cannot replace it.

The transfer process exists to avoid exactly that. You apply to the new provider, they collect it from the old one, and the wrapper survives intact.

Cash ISA to cash ISA transfers must complete within 15 business days. UK Finance reports 87% finish inside seven working days. If yours drifts past that, chase it — the deadline is a rule, not a target.