I’d say Major is the exception confirming the rule.
Brown went to Edinburgh, one of the best universities in the world; Wikipedia says there he had a fling with a Romanian aristocrat in exile, not exactly hoi-polloi. He then exploited his position in the Blair years as a political bridge between reformers and traditionalists in his party, and once PM didn’t last a single election. In a way, he was the best example of aggressively selective education as a vehicle for social mobility, which is funny if you consider that the staunchest supporters of such positions literally hate his guts. In any case, the Scottish Labour Party of the '80s was something very unique in the UK landscape, and doesn’t really exist anymore.
