In minor ways, European makers continued to use wood, mainly plywood, into the 70s and later. Three examples come to mind:
1. We had a Volvo station wagon, 1973 year, that used plywood for the panels that covered the storage well in the back (and that could be replaced by similar panels, with upholstery on them, to make a back seat).
2. My son briefly (thank goodness) owned a Triumph Spitfire* on which the "firewall" between seats and the gas tank right behind the seats was 1/2" plywood, and the dashboard was slightly thicker plywood. I don't know if newer Spitfires upgraded to metal, but the line continued until 1980.
3. I'm not sure when Saab stopped using little blocks of plywood on a metal rod to adjust the back seat height, on the Model 96, another vehicle that continued in production until 1980.
*which rapidly acquired another name, spelled just like "spitfire" except for the substitution of one letter, right after the "S," that more accurately described it. I was so glad that he never actually drove that frightening little car on the road, at least not much.