I believe banks must now give 60 days' notice before any increases to your rate can take place, so I'll assume this has been done.
There is an overriding requirement for all financial services companies of Treating Customers Fairly (TCF). It may be your provider has reviewed your credit score and decided it warrants a higher rate. Under TCF, it should provide more details about how it has reached its decision.
Contact it again with a firm but polite written enquiry as to the reasons behind your new rate. You could even explain this higher rate makes things much more difficult for you to repay, and it is possible RBS will revert it to your previous rate.
If it still refuses to give more information, write to its compliance department with full details of your request for clarification and its refusal.
Your ultimate recourse is to the Financial Ombudsman, which would consider whether the provider has acted properly and whether you have been disadvantaged financially as a result of the bank's action.