I wouldn't say Scotland was particularly left-wing, although from my experience of living there, free-market liberalism isn't popular. It is just that the dynamics of party support in Scotland tend to shut out right-wing representation.
The Scottish Unionists were the most powerful political group in Scotland until the 1960s. Then, for reasons best known to themselves, they amalgamated with the Conservative Party and have shed support ever since, being seen as an increasingly thin end of an English wedge.
Had they remained independent, I expect they would not have ended up being so associated with the English nationalism that pervades the Tories today.
The Scottish National Party were also right-wing: in fact they were nicknamed the Tartan Tories. They changed tack, but managed to retain their strong support in rural areas previously held by the Conservatives.
There is a centre-right vote out there in Scotland, but it is (extremely ironically) stitched up by the SNP and what remains of the Conservatives. In the meantime, right-wing Scots who in other circumstances might be political leaders in Scotland simply head south.
The situation is in fact the reverse of the situation south of the border, where the centre-left vote splits between Labour and the Lib Dems leaving the Conservatives a clear run on the right... until now, that is.
My chief memory of living in the place is an overwhelming suspicion of anything from England, similar in fact to the English suspicion of Europe. Euroscepticism is out because it's English. Identification with right-wing politicics is out because it's English. Free market liberalism is right out because Thatcher was English. I wonder how things would have been different had she been Scottish.
I am English but have spent half my life living elsewhere and now live in NZ with my non-English DW. While I did have a some unpleasant experiences, including nearly being beaten up, my chief memory is feeling like I had some kind of birthmark on my face, identifying me as English, and everyone noticing it; never ignoring it, never allowing me to fee like I was being treated as just myself. I have never felt that way in any other place (I've also lived in SA).