Why do men in the UK call girls birds Watch
(joking on the last 2 points - girls are lovely )
Actual answer (ripped off Google): As early as 1300, bird was used for ‘girl’, but this was probably owing to confusion with another similar middle English word, burde, which also meant ‘young woman’. The usage crops up from time to time in later centuries, clearly as an independent metaphorical application, but there does not really seem to be an unbroken chain of occurrences leading up to the sudden explosion in the use of bird for ‘young woman’ in the 20th century.
Oxford dictionary of Word Origins says that the British slang use of bird to mean a young woman is associated with 1960s and 1970s but as you mentioned also, it dates back to Middle Ages. It also adds that the Virgin Mary could be described in those days as "the blissful bird of grace." The modern use appears to be something of a revival.