Question in the subject... Thanks!
That would depend upon your skill at interpreting languages. English is recognizable to the observant eye all the way back to Old English, but it gets increasingly difficult to understand without knowing specific Lexis and Grammatical variations.
Any time after the introduction of the Printing press by Caxton to Westminster (1476) would mark the beginning of English's standardization and eventually becoming what we have today. This is from The Millers Tale from Chaucers canterbury tales circa 1340-1400 This about as far back as the average person would be able to interpret:
"This clerk was cleped hende nicholas. Of deerne love he koude and of solas; And therto he was sleigh and ful privee, And lyk a mayden meke for to see. A chambre hadde he in that hostelrye Allone, withouten any compaignye, Ful fetisly ydight with herbes swoote; And he hymself as sweete as is the roote Of lycorys, or any cetewale. His almageste, and bookes grete and smale, His astrelabie, longynge for his art, His augrym stones layen faire apart, On shelves couched at his beddes heed; His presse ycovered with a faldyng reed; And al above ther lay a gay sautrie, On which he made a-nyghtes melodie So swetely that all the chambre rong; And angelus ad virginem he song; And after that he song the kynges noote"
This is Anglo-Saxon Old English, and is basically a separate language by this point, you might be able to understand the odd word. The unusual Letters ð (eth) and þ (Th) are remnant runes still used for those sounds at the time.
"Wrætlic hongað bi weres þeo frean under sceate foran is þyrel bið stiþ ⁊ heard stede hafað godne · þonne se esne his agen hrægl ofer cneo hefeð wile þæt cuþe hol mid his hangellan heafde gretan þæt he efe lang ær oft gefylde"
I'd approximate that your average modern Londoner would be able to pick up the differences in language about as far back as the 1350's and awkwardly converse.