The Norman conquest meant that for 300 years English virtually ceased to be a written language, with both literature and administrative documents being written in French or Latin. So we simply have no idea how quickly it developed from Anglo Saxon into Early Modern English. However, what little evidence there is seems to put the change later rather than earlier.
According to Wikipedia's article on Middle English, the period 1100-1300 saw English retain the vocabulary of Old English almost intact, but simplifying the grammar significantly. Old English was an inflected language with lots of case endings, for instance (a dative case, a locative case, etc) but these were abandoned and replaced by prepositions and word order instead.
Then in 1300-1400 - the time when the English aristocracy were starting to speak English instead of French - the change became much more dramatic, with a lot of Old English vocabulary being dropped and French or Latin loan-words coming into the language instead. Chaucer wrote in Middle English (around 1380) but it's much easier for modern English-speakers to understand his work than it would be to understand something written just a hundred years earlier.