My fiance's dad was born in Cambridge (UK) while his dad was in the US airforce and his mom was a local (UK born). Would he qualify for a visa based on his dad's place of birth and grandmothers? His father's birth certificate states that he was born in Cambridge instead of an air force base. And my fiance's grandmother lived in Wimbledon until she moved to the US. I'm not sure what the rules would be for visa requirements are in his case.
The status of his parents isn’t quite clear. If his mother was “a local born in the UK” and it means she is a British citizen, then the son inherits British citizenship from her. He is British. If he was himself born in the UK, then he is British citizen “not by descent” and his children inherit British citizenship from him. If he is born outside the UK then he is only “British citizen by descent” and his children only have British citizenship if they are born in the UK.
Since his father isn’t British, it doesn’t matter where he was born as far as UK citizenship is concerned.
Sorry, got confused. All the above actually applies not to the fiancé but the fiancé’d dad. It seems your fiancé’s dad was British not by descent, which makes the fiancé British by descent. He is British citizen. He can just get a British passport. And about the only people in the world who can’t get a UK visa are British citizens - because they don’t need one.
I want to add some comments regarding whether your fiance has British citizenship. You said your fiance's father was born in 1956, and normally someone born in the UK before 1983 would automatically be a British citizen (or the equivalent previous status that converted into British citizen) by birth. And your fiance would also be automatically a British citizen by descent, due to being born to a father who was a British citizen otherwise than by descent.
One of the other comments mentioned the possibility that your fiance's father had diplomatic immunity. Under section 4 of the British Nationality Act 1948, someone born in the UK does not have British citizenship if "his father possesses such immunity from suit and legal process as is accorded to an envoy of a foreign sovereign power accredited to His Majesty, and is not a citizen of the United Kingdom and Colonies".
I am not sure whether people in the Air Force got immunity from suit and legal process. That's the first thing you need to determine. If your fiance's father didn't have immunity, then both your fiance's father and your fiance would definitely be British citizens.
In the unlikely case that your fiance's father did have immunity, and thus he didn't have British citizenship (and your fiance wouldn't have gotten it at birth either), it gets a little interesting. It is possible that section 4L of the British Nationality Act 1981 (which was recently added by the Nationality and Borders Act 2022) would allow both your fiance's father and your fiance to register as British citizens using form ARD.
This provision allows someone to register as a British citizen, if they would have been a British citizen if it were not for "historical legislative unfairness", which specifically includes any nationality law that treated males and females unfairly. The tricky part in this case is that it's not clear what the law would have said if it had "treated males and females equally".
One way to make the law equal would be to say that a child born in the UK did not have British citizenship if either parent had immunity. That formulation would not help your fiance's father or your fiance. However, another way to look at the law is that if only the mother had immunity, and not the father, the child would have British citizenship, so another way to make the law equal is to say that if only one parent had immunity, and the other parent didn't, the child should have British citizenship. That would allow both your fiance's father and your fiance to qualify. It's kind of a stretch, but it's logical that this law should allow them to register in this case, because if the genders had been switched (i.e. if your fiance's father had a mother who had immunity and a British father), your fiance's father and your fiance would indeed already be British citizens.