Yes, these records are available to the public but, access may be limited to professional researchers in many cases. You can hire one or if you have your grandfather's full name, service number, date of birth, etc you can request a copy of his full service record through a Freedom of Information Act Request which the government will fill. Unit records are best gotten using professional help if you don't know how to do the research as the record system is huge and somewhat confusing. You would also need some idea of which series to start in.