Ethnicity is not determined by a passport. The "ethnos" is a group of people of common descent with a common language and culture. Its a Greek word, but the same thing as nationality, coming from the latin root "natus", "to be born". If you are born an ethnic related to the people of Pakistan and India you can never, ever, ever become a Briton, just as you could never, ever, ever become an African or an Australian Aboriginal. Its as impossible as homosexual marriage.
I have as much chance of turning Chinese as anyone from the subcontinent has a chance of ever being mistaken for an actual Briton.
And no, it doesn't matter how many generations you are there. Unless they intermarry and gradually lose their "Indianness" or "Pakistaniness" over perhaps 5 generations (the old 1/32 rule) of marrying Britons, they and their children ain't Britons!
A Passport stamped "Briton" makes you a British citizen, not "British". Nothing more, and nothing less.