Assuming the flights are on a single ticket, Best option is to go to Flight connections. They will already have your new flight info, booked hotel (usually Premier Inn on Bath Road), vouchers for dinner and breakfast, vouchers for hotel shuttle.

If your family member has no visa to enter the U.K., they will also provide necessary paperwork to allow entry into U.K. Additionaly they also used to provide an overnight pack.

Note that flights from India have a large number of passengers connecting through LHR to USA, BA are used to handling this at flight connections And also a large number of wheelchair assistance passengers.