Generally you'd set up a Premier account in the UK first. Once that's set up they can assist you in opening an account in another country. The minimum relationship balance in such a situation would only apply to your UK account.

In my case, my primary account is in Canada so the minimum relationship balance is CAD 100 000.00. I subsequently opened an account in the USA, but only keep about $50 in that account on a regular basis. For a number of reasons I've avoided opening a Premier account in Hong Kong, but if I do there will be no minimum balance on that account either.