Learn English – “You are likely to [verb]” vs. “you are like to [verb]”

In a recent answer to another question, a fellow poster just used the following turn of phrase:

The nearest you’re like to get is [word][.]

I only ever saw and used "you’re likely to…" myself, but something told me it wasn't a typo. So I started looking around and sure enough it wasn't. After some discussion in chat, here's what we have determined so far:

• 50–60 million Google hits for "you are like to"; 3 million for "you are like to get". (120 million for "you are likely to", 11 million for "you are likely to get".)

• 2 hits on BNC, 0 on COCA. The poster is from the UK. Seems to be a British thing. More stats follow:

                         COCA   BNC
  you are likely to [v*]  150   167
  you are like to [v*]      0     2
  we are likely to [v*]   126    67
  we are like to [v*]       0     0
  I am likely to [v*]      18    12
  I am like to [v*]         0     1

  Until we come to this outlier:

  he is likely to [v*]    143    92
  he is like to [v*]        2     1

  The two COCA cites looking legit:

  • There's a danger that some of the weapons of mass destruction he is like to have had may have leaked out of the country.

    — SPOKEN, 2003, CNN.

  • A Californian! This is herring man, a favorite to vodka. He is like to have hammer and sickle tattooed on his chest.

    — FICTION, 2001, Harper's Magazine.

• Some hits on Google Books. For example, from Burke, Paine, Godwin, and the Revolution Controversy, Marily Butler (ed.), 1984:

  Can I be blamed to point out to him in what manner he is like to be affected, if the sect of the cannibal philosophers of France should proselytize any considerable part of this people, and, by their joint proselytizing arms, should conquer that Government, to which his Grace does not seem to me to give all the support his own security demands?

  Again, Cambridge University Press, so could be a British thing, if not for the spelling of proselytize that suggests otherwise.

• The quick straw poll in chat produced reactions ranging from "Really? Never heard of." through "It's an odd one. I suppose it's fine colloquially." to "I have heard this, and I think it is a modern mal-back-formation of likely when the sentence structure resembles a copula."

So, my questions are:

• Is this or is this not a strictly British thing? Does it sound grammatical to Americans? And what about Indian/Australian English?
• How recent is this use of like? Who knows — does it perhaps even predate the corresponding use of likely?