The myth

The British have been doing a Harvey Smith, flicking the V, and
sticking two fingers up since 1415. At the Battle of Agincourt (or
perhaps Crecy), the French threatened to cut off the English
longbowmen's first and second fingers, thus permanently disarming
them. When the English won a surprise victory, they waved their
fingers defiantly at the enemy.

The "truth"

No-one seems able to prove or disprove this popular story, but there
are a lot of reasons to doubt its veracity. According to
anthropologists, hostile gestures involving jerking movements of
parts of the hand or forearm are found in many, if not most, cultures.
There's no record of captured bowmen being mutilated at Agincourt,
or elsewhere; if the practice had been widespread enough to launch
the V-sign, such records would surely exist, from a time when all
aspects of warfare were closely scrutinised and chronicled.