Upvote:2
Michael Hampton's answer is incorrect. "Pakistani origin" does not just mean "born in Pakistan". Having a Pakistan-born father counts as being of Pakistani origin in this situation no matter your country of birth and citizenship. You can still apply for and eventually receive an Indian visa but you can't apply for an e-visa and you may experience significant delays.
Upvote:4
Yes, you can apply for and obtain an Indian visa even if you or your parents are of Pakistani origin. (Note that "Pakistani origin" means "born in Pakistan".)
Since you are a British citizen, and not of Pakistani origin, you can even get the new e-Tourist visa, as late as four days before your arrival.
However, the e-Tourist visa is not available to people of Pakistani origin, regardless of their passport, so the father would not be able to get one, and would have to apply for a regular visa.