Common on both sides of the pond, of course. OED’s earliest cite is the title of a Gus Kahn song in 1932 but I’m sure the usage could be predated easily. Here’s what I find mildly interesting though. I watch a lot of 30s US movies, especially pre-code. The phrase crops up frequently in these films but almost without fail it’s spoken as an interrogatory, with a slight stress on the me: You’re telling me?
I’m not reading too much into this but as I say I did find it mildly interesting. I always hear it as an exclamation now and none of the OED cites illustrate the interrogatory usage.