HiMy particular source said "from about mid-1940" without additional details. The Battle of France began on May 10 and ended June 22. The Battle of Britain is given officially as July 10-October 31. Additional particulars would be welcome, although the main point remains, that Spitfires did not have armor until after the RAF gained some combat experience.
More information from Fox's book:
From this it appears that all the original Hurricane squadrons in France had been fitted with rear armour plate before 10th May 1940, indeed all new production Hurricanes had been fitted with same from 22 February 1940. Most discussion is on retrospective fits on aircraft in service the same applies to mods like Constant Speed propellers which were introduced on 'new' production (Hurricane production from October 1939) and then there was catching up mods to do on squadrons and MUs on aircraft already delivered.
There is some discussion on Spitfire rear armour as there had to be some redesign in the cockpit (one item was the pilot's head rest) to fit it which would slow up production of the aircraft. However, decisions had been made about rear armour for both Hurricane and Spitfire prior to the experience of the Battle of France.
Mike