British Protected Persons (BPPs) were not British subjects, CUKCs (Citizens of the UK and Colonies) or British citizens. BPP status was also lost on acquisition, voluntary or otherwise, of another nationality. So, I doubt if you would have acquired any claim through your ancestors working or living in a British protectorate.
Check your grandfather's and great-grandfather's British passports to see if they were issued to them as BPPs or if they registered as CUKCs. If the latter, that changes the situation considerably.
Also see
similar case and revert with any further questions.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.