Far from a "how d'you do?," the chances of Morgan being right with his guess are slim to none. Nevertheless, in Tony Blair's memoirs, A Journey, he recounts a very similar interaction.
The Telegraph reports that Blair remembers the Queen telling him: "You are my 10th prime minister. The first was Winston. That was before you were born." Could it be possible that this is correct?
Morgan says: "I wish I could pretend that I had inside knowledge, but I made up those lines. No minutes are taken of meetings between prime ministers and monarchs and the convention is that no one ever speaks about them, so I didn't even attempt to find out what had been said."
He offers three possibilities. He somehow guessed the almost exact exchange, which is "highly unlikely." Or, maybe "Blair decided to endorse what I imagined as the official line." And the last option, Blair confused the movie dialogue with his own memory. While the last seems the most likely (if we're not assuming Blair stole the line for his memoir), there is a problem with it -- the ex PM swears he's never seen the film.
You gotta watch those memoirs. Minds and egos like to play tricks. And if it's neither of the above, Morgan should look into a career change. He'd make one hell of a psychic.