Interesting piece in the guardian some days ago:
Mark Stephens, an acknowledged legal expert on diplomatic immunity law, challenged whether Jonathan Sacoolas enjoyed full immunity under the Vienna convention, saying he had not been registered as such with the Foreign Office.

He suggested Sacoolas and his dependents instead only had more limited immunity under the Visiting Forces Act, and its derivative bilateral orders that provide immunity to personnel on specific UK bases. That immunity, according to Crown Prosecution Service guidance, is restricted to specific offences that “arose out of and in the course of the service person’s duties as a member of the visiting force including whether the act occurred in the course of the individual’s professional duties”.

The US air force has in the past, according to the CPS, interpreted professional duties to include driving from an air base to a home address. The Sacoolas family was reportedly living on the base, which would mean they could not claim that defence.