From what I've understood, German helmets were the most efficient and protective, also American M1. Why did British troops keep using an outdated helmet from one war to the other?
The British did update their helmets during WW2, the Mk.II Brodie had a better chinstrap, and a new shell. The fact that they were of a practically identical shape means that they were good enough for the job, just because the design was the same as that used in the First World War, it doesn’t mean it was obsolete. For example, the French and other nations continued to use Adrien helmets between both wars, and the US made use of Brodie helmets throughout WW2, too.