UK bank account

Without a permanent address there, opening a new account is pretty much impossible.

I have had a UK bank current account since I was a teenager. I have never closed it although I am now a permanent resident in Belgium.
I wanted to open a second, savings, account with my bank but I was not allowed as I have no permanent address in UK.

The UK has no formal way of keeping tracks on who's who. That makes it attractive for illegal immigration and identity fraud, and causes things like banks to come up with some totally ludicrous ways of making sure who's who.

Try looking for something like a non-highstreet bank that deals with expats.

There is some factual information here. Believe me, unless you have some sort of formal proof that you are moving there, it's not easy and you may have to go with an offshore bank instead,
.
http://moneyfacts.co.uk/guides/banking/can-you-open-an-account-without-p...

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