Depends on where you went how and good you are with accents. You'd start noticing a clear issue before 1700, the end of the Great Vowel Shift, and that will get more pronounced as you go further back in time. You might start having trouble as early as the late 16th/early 17th century: here's what Shakespeare sounds like in the original pronunciation. Assuming for the sake of convenience that you stay in England (Scotland is much harder if you're from England and especially if you're from America) , you'd start having serious issues by the fourteenth and early fifteenth century, but again it depends on where you go. English isn't divided just by accents at that point but into dialects with different pronunciation, grammatical construction, case endings, vocabulary, and even letters.

For example, Chaucer and the Pearl Poet were contemporaries in 14th century England, but the former wrote in a London dialect and the latter in one of the NW Midland.

Here's the opening to the Canterbury Tales:

Whan that Aprill, with his shoures soote

The droghte of March hath perced to the roote

And bathed every veyne in swich licour,

Of which vertu engendred is the flour; 5

Whan Zephirus eek with his sweete breeth

Inspired hath in every holt and heeth...

And here's what it sounds like aloud.

By contrast, here are the opening lines to the Pearl Poet's Sir Gawain and the Green Knight, written around the same time:

SiÞen þe sege and þe assaut watz sesed at Troye,

Þe borȝ brittened and brent to brondeȝ and askez,

Þe tulk þat þe trammes of tresoun þer wroȝt

Watz tried for his tricherie, þe trewest on erthe:

Hit watz Ennias þe athel, and his highe kynde,

Þat siþen depreced prouinces, and patrounes bicome

Welneȝe of al þe wele in þe west iles.

And here's what that sounds like aloud.

Now let's move back to the 13th-century Katharine Group, saints' lives written in the West Midlands:

(1) Costentin ant Maxence were on a time as i keiseres stude, hehest i Rome.(2) Ah Costentin ferde thurh the burhmenne read into Franclonde ant wunedesumme hwile thear for the burhes neode, ant Maxence steorede the refschipe iRome. (3) Weox umbe-hwile wreathe ham bitweonen, ant comen to fehte. (4) WesMaxence overcumen ant fleah into Alixandre.

Or the Ancrene Wisse, also West Midlands but a little bit earlier:

"Laverd," seith Godes spuse to hire deore-wurthe spus, "the rihte luvieth the." Theobeoth rihte the luvieth efter riwle. Ant ye, mine leove sustren, habbeth moni dei i-craveton me efter riwle.

Another 70-odd years takes us to the Ormulum of the mid-12th century, written in an East Midlands dialect:

Forrþrihht anan se time comm  þatt ure Drihhtin wolldeben borenn i þiss middellærd  forr all mannkinne nedehe chæs himm sone kinnessmenn  all swillke summ he wollde & whær he wollde borenn ben  he chæs all att hiss wille.

I think you're well past out of luck at this point.

Of course, these are all literary examples, written for an educated audience. We don't really have many records of how ordinary people spoke in medieval England, but it will give you a pretty good idea of where your comprehension and ability to communicate would fall off.