Workwear was lined. Jaeger, Planet, Alexon, Austen Reed, Windsmoor, Paddy Campbell etc, etc even Laura Ashley did wool crepe or light wool gaberdine dresses and skirts which were always lined. Laura Ashley was the cheapest of those brands, but still not cheap. The others , apart from Paddy Campbell, were upper level high street- Paddy Campbell was pricey.
Posters go on about The Fold for workwear. Some of their dresses are lined; none of them are pure, or even mostly wool.
Some evening wear was lined. I had silk, non work day dresses from Laura Ashley which were lined and they also did lined non work silk skirts. Brora did lined silk dresses.