Minis are and were "regular" transportation in the UK. Hence they sat outside and were subjected to normal wear and tear. You'll find these cars for sale right next to restored cars. Don't think for a moment that they are all showpieces. I have seen a number of so-called "rust free" cars come across the pond only to immediately go to the body shop for rebuild! (Apparently the phrase "rust-free" is open to conjecture or doesn't have the same meaning as it has here) So, yes you can find some inexpensive cars in the UK, including a few genuine bargains. However, I wouldn't buy a car from across the pond without seeing it first. That is too much like purchasing a pig in a poke.
I see you're in Canada. You have a genuine advantage over those of us further south as Minis were imported and sold in Canada untill 1980. There are many of these available and (from my point of view) seem to be as good a bargain as the UK cars. I would stick to the ones I can see and touch to be sure they are of acceptable quality.
Done properly, shipping, taxes, duties and registration can cost upward of $1500.00 to get a Mini from across the pond. Have you added that to the costs of purchasing a car from the UK?