Ok it's fair to say my answer was a little bit misleading to quite an ambiguous question. I did say usually and then added in the end that the bank doesn't really care if you choose to keep your money with them! But I guess that was lost somewhere...

I have also kept a couple of accounts in the UK, but I still maintain an address there so can't really say for sure.

The terms of certain accounts is that you have to be a UK resident or at least have a UK address, some banks might not enforce these rules religiously and you might find that you indeed will be allowed to open new accounts, top up old ones, or even top up your existing ISAs.

Might seem a bit of a joke, but you will get close to a big fat ZERO here in Switzerland, so nothing in the UK is better than nothing in Switzerland