Interesting.
From Wikipedia re Hawker Hurricanes with same two-blade prop issue:
Accordingly, trials with a de Havilland variable-pitch propeller demonstrated a reduction in the Hurricane’s take-off run from 1,230 to 750 ft (370 to 230 m). Deliveries of these began in April 1939: this was later replaced by the hydraulically operated constant-speed Rotol propeller, which came into service in time for the Battle of Britain.
When Chamberlain was in Munich, the Luftwaffe was just introducing the Bf-109E with the DB 601. The current service versions (A-D) were using 660–690 HP Junkers Jumo 210 series engines.
The Spitfire Mk1 would have handled the earlier versions Bf-109 quite harshly, wooden prop or no.