I summarized the issues you would run into a few weeks ago https://m.reddit.com/r/AskHistorians/comments/55utij/comment/d8e87t7

The history of English is typically broken into 3 main phases:

Old English (OE) pre-1100

Middle English (ME) 1100-1550

Modern English (ModE) 1550-present

They can all be subdivided further, but the only that's particularly relevant to this question is Early Modern English (EModE) which is generally dated to 1550-1700.

The three main issues you would run into when understanding past English speakers vocabulary, phonetics, and syntax.

The vocabulary of English hasn't undergone any major changes since ME. In OE, the vocabulary was almost entirely of Germanic origins, but after the Norman conquest a lot of words of Latin origin were brought into English both from the Norman dialect of Medieval French and directly from Latin. These Latinate words completely replaced many corresponding words of Germanic origin or supplanted the Germanic rooted words in certain idiomatic contexts. A prominent example of Latinate and Germanic roots coexisting would be how agricultural terms typically have Germanic roots, but culinary terms typically have Latinate roots. So you raise a "cow" (Germanic root), but you eat "beef" (Latinate root). This is since the Norman elite would have had more interaction with the chefs who worked in their kitchen than with serfs who actually did the agriculture. Despite this flood of Latinate words into English which actually now form the majority of the English lexicon, most of the Latinate words in English are more obscure, to the point that 100 most common words are all of Germanic origin.

While you might sometimes hear that something like 10% of English words were coined by Shakespeare (in the EModE era), that is actually the percentage of English words that were once thought to have been originally attested in Shakespeare. This means that the word might have been spoken for a long time before someone wrote it down. Computer searchable databases of English texts has also significantly reduced the amount of words thought to be first attested in Shakespeare.

While the vocabulary of Modern English can mostly trace its roots to ME, that does not mean that the typical English speaker would easily pick out the vast majority of words spoken c.1400. Differences in pronunciation and a different case system and a different subject-verb agreement system would also pose difficulty in with intelligibility. There have also been smaller changes vocabulary and idiomatic meaning during ModE, but to a much smaller extent.

The major changes in phonology also happened in ME. The most notable changes would be the Great Vowel Shift which occurred during the 15th and 16th centuries. This change had a massive effect on English by completely changing Engl8sh long vowels and is generally considered the divider between ME and ModE, but some English speakers would have persisted with certain pre-Great Vowel Shift vowels into EModE. Other major phonetic changes were open syllable vowel lengthening, the loss of word final "e" (now known as "silent e"), the split of voiced fricatives (v and z) from voiceless fricatives (f and s), and the loss of palatal and velar fricatives which used to be denoted by gh in words like night and rough (this change also persisted into EModE). There have been other phonetic changes that occurred in ModE, but they are either do not affect many words (such as dropping the k at beginning of words like knot or knight) or are only regional variations (such as non-rhotic, aka r-dropping, accents) and most current English speakers will be familiar with both forms.

The major changes to syntax also occurred during ME, but many of them persisted through EModE. This could have been from a minority that hadn't made the switch, some speakers viewing both as correct and using both forms interchangeably, or the ME form being used archaism. These changes included the transition of English from Germanic Verb-second word order to Subject-Verb-Object word order, the beginning of do-support, the loss of case grammar outside of pronouns, the simplification of the subject-verb agreement system, and the introduction of the Norman genitive. Once again, there have been smaller changes in syntax since then. These include split infinitives, using indicative forms for the subjunctive (ie many people consider "If I was wet" an acceptable alternative to "If I were wet"), and using "who" as an object.

Where exactly you go would also affect the language barrier. Modern English is generally considered to have developed in English port cities and spread from their due the relative influence of those cities. So you would have to go further back in those cities to start encountering a language barrier than you would with rural inland England.

Since there are of course no accounts of someone from modern times speaking to with someone from, say, Tudor England, any answer about exactly how problematical these changes would be and when they would begin to be too much would involve some speculation, so I won't go into that here. If you're interested in people knowledgeable on the subject speculating about those answers, r/linguistics might be helpful.

One thing I would like to add is that people understanding you would likely be a much bigger problem than you understanding other people. Modern English speakers receive a decent amount of exposure to EModE, but an EModE speaker has never been exposed to ModE.

There's always room for discussion, but perhaps the section How far back could I go and still communicate? from our FAQ will answer your inquiry.

It wasn't easy to communicate in pre-industrial England, as the English language was fractured by many, many dialects.

This would have been your biggest problem -- going from region to region, as the dialect could easily change within a distance of 20 miles (or 30 km).

After the development of the industrial revolution, which saw more and more people move into the cities in search of work, did the English language start to standarise more and more, to the point where the language became far less fractured by dialects.