Per tax year (which runs from 6 April of one year to 5 April of the next year), you are restricted by the ISA allowance as to what you can put away. For both the 2018/19 and 2019/20 tax years, the ISA allowance stands at £20,000.
This means that you can put this amount of money into a new or existing variable rate ISA. If you also want to save in a different kind of ISA (say a stocks & shares ISA), you should note that the allowance covers all of them combined. So, if you want to save in both a cash ISA and stocks & shares ISA, you’ll have to decide whether you want to put an equal £10,000 in each account or divide the funds up differently.
While you’re only able to put a certain amount of new money into an ISA per tax year, you are able to transfer your existing ISA funds across providers without limit. So, if you see a better variable rate elsewhere, you should be able to transfer your whole pot over in one go – just be sure to follow the ISA rules, otherwise you might end up getting in trouble. Bear in mind that not all ISAs allow funds to be transferred in, it depends on the provider.