I have watched this thread with interest before replying.
I looked through all the T&Cs of my own bank (not RBS) and couldn't find a single thing that says you have to be ordinarily resident in the UK to open an account. There's several clauses that apply only to UK residents - for example related to payment of interest with / without deduction of basic rate tax, or what happens if you are declared bankrupt in the UK.
So I suspect the generic answer is that there is nothing that requires a UK address, HOWEVER it is entirely up to the bank if they will accept your application for an account, and the terms (invoking banking charges) under which they will accept it.
A family member lived permanently abroad (UK passport-holder as it happens, however that's irrelevant to this) was able to hold onto her UK bank account for many many years by keeping to the address that was registered in the UK - but when that property was sold and she had to concede she had no UK address anymore, the bank wanted the account closed. This was Lloyds-TSB.