English has changed tremendously from Old English to Modern English. Which intermediate versions are considered to be mutually intelligible? For that matter, what about asymmetrical intelligible?
I would like to say that Chaucer is a marker and significant contributor to the gradual shifts towards the more intelligible Shakespearean English.
Chaucer and his compatriots, and Chaucer himself in no small measures, had contributed to the solidification of the English dialect in London. Chaucer himself contributed to the importing of continental European and Latin structures due to his translation and plagiarising of stories from continental Europe. It was also very helpful that the English monarchy had somewhat rewarded poets and writers. Chaucer's having been a government official in various capacities as well as having been a parliamentarian would have had significant influence on the literature among traders and the general population.
The black death of the 14th century coincident with Chaucer's period which resulted in both social strata mobility and geographical mobility of the British population should be considered to have sped up the change from older forms of English to Shakespearean.
The black death had also created vacancies in British aristocracy and nobility, such that French was displaced by Chaucerian English as the lingua franca as well as the native language among the aristocracy and nobility, due to the movement of English speakers into those vacancies. Hence, retaining the tendency of English to have French language elements.
The black death in combination to coincident political upheavals that had encouraged population and social strata mobility should be considered as the main contributors to the great vowel shift. Changes in pronunciation of the English language would also have affected changes in the way words were spelled.
Old English mainly being of Nordic and Germanic origin was dialectically dependent on regional immigrant composition. The black death and Chaucer's period collaborated to compose a new English language structure within the literary and political power centre of London, culminated by the great vowel shift.
IMO, most of the population during Chaucer's time would not understand modern English. Especially that a significant portion of the literate population were speakers of French. Conversely, most modern English speakers would find Chaucerian English unintelligible.
Whereas, native Shakespearean English speakers and modern English speakers would have a high degree of mutual intelligibility.
In the generation after Chaucer, William Caxton bringing the printing press to England contributed to the further solidification of the English language. William Tyndale's publication of his English translation of the Bible would have exploited and propelled the use of Tudor English immediately after the great vowel shift.
I would say that the earliest form of English that is mutually intelligible with modern English would be Tyndale biblical English. I think that the comprehension would be more asymmetrical in favour of modern English speakers understanding Tyndale English than the other way around.
We would be able to take a sample of modern English speakers to test the hypothesis, but it is certainly impossible for us to take a sample of Chaucerian or Tyndale English speakers (until the technology of time travel is available to modern English speakers, where such an event itself could be 1000 years away in the future).