Take my primary school. In the late 1960s, and perhaps still (although the place now looks very different), we had four school houses: Scott (after Captain Scott), Nightingale (after Florence), Nelson (after Horatio) and, er, Berthon (of whom more below).
This particular set is redolent of Britain's imperial heyday, but I'm guessing that the inclusion of Scott puts 1912 as an earliest date. Beyond national pride, there seems little specific reason to pick on him: he had no local connection that I'm aware of. No more did Nelson, really, although the Victory is at least moored in the same county. Florence Nightingale was a local based at West Wellow, four miles or so outside the town. And Berthon? Well, he was so much a local that no one outside Romsey has really heard of him, I think.
Okay - that's not quite true: Edward Lyon Berthon (1813-99) does have a Wiki page, but he's not in the same league as the rest - even if he holds the distinction of having amused Queen Victoria. He was vicar of Romsey, but had a nifty sideline in boat-building, being the inventor of a collapsible life boat. The Berthon Boatyard has long since moved to Lymington - which has the advantage, for a boatyard, of being on the coast - but I noticed as I walked through the car park behind Portersbridge St the other day that there's still a plaque on the old site. (A few yards away is another plaque marking the house where Sir William Petty was born: if I'd been choosing school house names I might have gone for him, although I admit his surname doesn't lend itself to enthusiastic chanting at sports days.)
So, I reckon the naming happened later than 1912, when Scott was martyred by the ice, but probably earlier than 1918, when Harry May bought the Berthon Boatyard and moved it to Lymington. In between sits the Great War, which we might expect to have had a gravitational pull on the choice of house names in itself ("Wot no Kitchener?"), so my best guess is that the houses got their present - or at least still-current-in-the-1960s - designation circa 1913.
(At secondary school the houses were named less interestingly, after large local houses. I was in Roke, after Roke Manor, which is now an R&D place for a multinational electronics company. When an old schoolfriend became MD there, I congratulated him on being made Archmage, but I'm not sure he got the reference. Still - Roke was the coolest of a bunch of very dull names.)
Anyway. You see what I mean about the time capsule idea? Of course, not all schools have houses at all, but that in itself tells us something - specifically that they were founded at a date when competition was anathema in educational circles.
Meanwhile, in my daughter's school (founded some six years ago), they have a complicated system worthy of Linnaeus, in which all the children are divided into Waterfowl and Songbirds. There are further subdivisions beyond that (Ducks, Geese and Waders, iirc?), but suffice it to say that my daughter has spent her school career as a Gadwell. I'm sure we can all get behind that.