They used to be extremely common because of the high danish car taxation. It certainly also helped, that the original base model, Fiat 124, was very popular in Denmark and that the VAZ 2101 (sold in Denmark as Lada 1200) was introduced while the Fiat 124 was still being made, but at a much lower price.
In 1973, a Fiat 124 base model was priced at DKK 32.000, while the Lada would set you back DKK 24.000. At this time, the Fiat had undergone a facelift, so at least the two didn't look exactly the same, but both had reputation of poor build quality and rust, so the Fiat didn't have much of an advantage there, so you would essentially save 25% by getting a pre-facelift version of the same car - on a market where cars were already insanely expensive.
Other cars costing approximately the same as a Lada 1200 in 1973 were: Citroën Ami 8, Fiat 127, Morris Mini 1000, Moskvitch 1500 Estate, NSU 1000 C, Renault 4 Luxe, Skoda 110 LS and VW Beetle 1200 base model. For most popular car makes, the cheapest models typically cost somewhere between DKK 26.000 and 30.000.