The difference is mostly quantitative. In USSR you could buy a car if you were willing to pay over MSRP (which was mandatory rather than recommended). Simply buy a new car used. Reselling your car immediately after purchase for a profit was a thing.
Some people (occupations such as arctic coal miner) had financial means to do so easily. Other people (notably, engineers on non-management positions like most of HN readers today) would never realistically afford one.
The choice was indeed very limited. But again, it is mostly a quantitative difference.
You know they say, quantity has a quality of its own
Don't compare UK shortages with what the Eastern Bloc went through. They had people going to surgery without anesthesia. You'll manage with your existing car for a bit more.