Locating Education Records as proof of residency in the UK

Hi all, we are trying to register our three children for British citizenship by descent based on the fact that my husband has British citizenship by descent and lived in the UK from 1981 to 1989. Although his father was in the US Air Force, he primarily attended English primary schools until the third grade and lived off base the entire time. We have a US passport that was issued by the US Embassy in London in 1982 that does not show any stamps for leaving the country until 1989, we also have a set of hubby's fathers orders listing my husband specifically, that shows him moving from UK base to another and he also has school records from where he attended american DOD school from the 3rd to the 6th grade. The area where we are having difficulty is obtaining any school records from UK primary schools. Have already contacted the Oxfordshire council and they advised no records existed that far back. Also contacted national archives who advise it was Oxfordshire who was responsible for keeping those records. Does anyone have any clues as to how to get this information. All I'm really looking for is proof of enrollment. Maybe there is something else I can use?

Maybe there is something else I can use?

His NHS records? Dental records? What evidence does the UK state is acceptable for registration of a child?

Not sure about his NHS records as most of his doctor visits happened on the American bases. I do have a little NHS appointment book for his speech therapy he did for a year in 1984. THe issue I'm running into is finding primary school enrollment records from the 1980's. Everyone asks like I'm asking for a two headed dragon when I tell them what I'm looking for I'm wondering if his American DOD schools will count as I have tons of report cards and progress reports from those for more than three years