The child will be a British Citizen (and therefore entitled to a British passport) if either, or both, of the parents were legally settled in the UK at the time of the child's birth (or if either, or both, hold British Citizenship).
However (quote): "Even if you were born in the United Kingdom, you will not be a British citizen if neither of your parents was a British citizen or legally settled here at the time of your birth. This means you are not a British citizen if, at the time of your birth, your parents were in the country temporarily, had stayed on without permission, or had entered the country illegally and had not been given permission to stay here indefinitely.":
http://www.ukba.homeoffice.gov.uk/britishcitiz enship/othernationality/Britishcitizenship/bor ninukorqualifyingterritory/
If the child is not eligible for a British passport, his/her parents will have to apply for an Indian passport for him/her. (In common with other countries, India no longer permits a child's name to be added to a parent's passport):
http://www.hcilondon.net/passport/registration -children.html
Chris