I've found that people who promote Blair and even Cameron as Scottish without mentioning that actually they think themselves English tend to be nursing a grievance against Scotland for whatever reason.
Otherwise we have Brown who was unequivocally Scottish and was often attacked on that basis during his premiership ("One-eyed Scottish Idiot" etc).
Otherwise in the 20th Century we have James Ramsay MacDonald (1930s for 6 years), Lord Douglas-Home (a year and a half in the 1960s), Henry Campbell-Bannerman (2.5 years), and Arthur James Balfour (3.5 years).
So 13 or 14 years of the 20th century, Britain suffered under Scottish prime ministers, only slightly above what we might expect given Scotland's share of the population of the UK - this could be explained by Scotland then-increased share of MPs.
It doesn't seem that Scotland dominates UK politics more than any other nation. However, it is certainly noticed and commented upon or even resented when Scottish people rise to high office, perhaps that's why it may seem so to some.
In the current political climate with the domination of the SNP, it seems like the possibility of Scottish MPs attaining any kind of high office, membership of the cabinet, or part of the governance of the UK has entirely vanished for generations with who-knows-what consequences for the union in the future.