The following is a wiki link to industrialisation in Germany which usefully compares the UK and German industrial revolutions. Germany industrialisation. The main message is that Germany lagged the UK for several decades, only beginning to catch up from around 1850-1870.
The UK was a complete and coherent nation for centuries with few internal barriers - legal, customs, communications etc. Germany was a set of separate states until unification in 1871. Much of its economic base was feudal in character and craft based.
Using iron or steel requires a sophisticated, integrated technological base (mining, transport, refining, casting, fuel, etc. As late as 1870s Britain produced over twice the steel of Germany.
It would have been a very expensive material only used if carrying very clear benefits over alternatives. Wood was cheap and techniques for working it established over millennia.
I know there are other views, but using steel and cast iron in making planes allows for a more consistent product with far less variation in quality and accuracy compared to wooden craft created alternatives - hence its almost universal adoption as the material of choice today.
