I mostly just know what I’ve read, to be honest, though I have eaten Cox and baked with what were supposed to be Bramleys (though they didn’t have the classic Bramley look to them). It seems like the big one is probably a traditional English cooker of some variety at any rate.
(As it happens, I experienced both Cox and Bramley as Scott varieties, in the sense that we got them from the Scott Farm orchard in VT. Never been to Scotland, though!)
My guesses are based on the premise that trees planted in the eighties were more likely to be standard UK varieties than unusual heirlooms, and Cox, Bramley, and James Grieve would fit the bill and seem to fit the descriptions given decently well. But you’re right that local guidance would be best.