The bank manager advised the best way to do this is to add to my folks mortgage
Funny that.
If I were you I'd get your name added to the electoral register then re-apply to the bank. With your income, and assuming you have a decent history with the bank, £15k over 5 years unsecured should be perfectly manageable. They would rather have it secured against property for obvious reasons.
If they still won't play ball, threaten to take your business elsewhere.