How far in the past was English understandable to me?

Before I ask my question, let’s get a few assumptions out of the way:

  1. I am an average American male who only knows American English, midwestern accent (though I am teaching myself Italian, albeit rather slowly).
  2. I have a time machine that will take me to London at any point in the past.
  3. I’m not worried about reading, only speaking/listening.
  4. I can understand an average Londoner in 2003. (please no “divided by a common language” jokes)

So now, how far back in time could I go and still communicate effectively with Londoners?

Just out of curiosity.

There was a great thread on this exact question just last week.Here