In the case of the officer class, and the rest of the English ruling class, yes. Certain "public" schools catered to military and civil service families without the means to afford the snootier schools. The United Services College in the amusingly named town of Westward Ho, was more or less run for that purpose ( Kipling, though not from a military family, went there). I'm trying to think of a famous British officer between the later Victorian era and WW2 who wasn't, and I can only come up with ( besides Churchill) Robertson, who rose through the ranks. You read about " Anglo-Indian" families where the older children were expected to fake letters to, and even play Santa Claus ( Father Christmas?) for, the younger children while their parents months post away.

Should add too, that some noncommissioned officers brought families overseas. I can't think of any concrete examples one way or another as far as where their children were schooled, however. A lot of "rankers' " sons followed in their father's footsteps...as rigid as the class system was well in to the 20th century, they weren't expected to gain much more than a primary school education in many, probably most, cases.