I remember a similar joke:

What happened to the car with the steel wheels, steel chassis and steel engine?
It steel wouldn't go!

At least it wooden't rust ...

I know I should feel sorry, but I just could not resist...

Ha!

Let me guess: His name was http://en.wikipedia.org/wiki/William_Rootes,_1st_Baron_Rootes , wasn't it?

(Blowing the dust off a very old joke..... ) The man who built a wooden car with wooden wheels and wooden tyres and a wooden engine - but then it wooden't move.

Another three created by a Chinese carpenter: http://www.carnewschina.com/2015/05/04/chinese-man-builds-electric-car-out-of-wood/

I know, was just looking for an excuse to upload my Morgan factory pictures.

I thought also about Morgan and about a lot of pre-war car makers, of course, but these cars were/are not made by carpenters

They've been doing it in Worcestershire for some time:



Though they leave the wood solely to the frame and make the bodies from aluminum: