By the way, probably the first Michael Caine impersonation, or at least the first that became popular, was done by Peter Sellers. I posted it here a long while ago. It's worth checking out, it's only 16 seconds but a hoot. (His catch-phrase for his impersonation, which tended to be picked up by others was to tell some arcane fact and then finish with, "Not a many people know that...")
I actually crossed paths with Michael Caine once. No impersonations were involved.
I was a tour guide at Universal Studios at the time (something I talked about here) and wanted to go down to the lower lot one day to watch filming. That was one of the perqs of the job -- sorry, I mean the only perq of the job -- but few guides ever took advantage of it. That might be because if you got permission to go to a soundstage you had to wear your tourguide uniform -- that doesn't sound so problematic, except that the uniform at the time was blue slacks and a bright pink shirt. You stood out sort of like a rhinoceros at Royal Covent Garden. I remember walking onto the soundstage, a nervous kid, and people would come up to me and say, "Oh, you must be the tour guide." Yeah, that was hard to figure out... Though they were all very polite and nice about it.
The only movie filming that day was The Island, a modern-day pirate story based on a novel by Peter Benchley (who had written Jaws), and the star was Michael Caine. I wandered around the soundstage, taking a look at the sets, which that day made up the interior of a ship. When I heard them call "Places, everyone," and were about to start filming, I quickly got out of anyone's way because I knew that most actors hate seeing anyone in their line of sight -- most especially anyone they don't know -- and can get upset, indeed some famously can go ballistic. I found some dark, deserted area, far away from where the crew was set up and hid in a back nook of the set, a long corridor ahead of me.
And to my horror, I saw that at the other end of the corridor was Michael Caine.
The scene they were about to film was ahead of him, and so his back was to me, as he was preparing by himself for his scene. My stomach sank, and my heart began pounding. I was praying he would stay looking that way. But alas it was not to be. He had to back up to make his entrance, and so, as I could see him mentally getting ready, he started moving backwards and then...turned around.
And there he was, about 30 feet away, staring down this otherwise, totally empty corridor at me -- some idiot, total stranger, a kid standing there in in a bright pink shirt and blue slacks, with a name tag. I held my breath, in part out of terror for what might happen, in part because I knew everyone is supposed to be absolutely silent right before filming, and in part because I was hoping that would make me invisible. It didn't. He saw me. It would have been impossible not to see me. And what he did is --
And then he simply turned back the other way, they called, "Action!", and he did his scene.
And I exhaled. And became a Michael Caine fan for life.
There are a lot of temperamental actors in the world. Michael Caine is not one of them. Here is Michael Caine, doing an impersonation of Michael Caine. (The "Sean" he refers to, I assume, is Sean Connery. And the other actor sitting with him is Billy Connelly.) But be sure to stick around to the end -- not that you'd leave early -- but he actually does do an impersonation of someone else.
But it's not as good as his Michael Caine.