I was recently talking with a professor at an American university who regularly brought students to London for study-abroad programs. (He’s now retired.) He said that by the end of the semester, his male students had always incorporated into their vocabulary three insults: wanker, tosser, and poser. I’ve covered the first here (and touched on it several other times: plug it into the “Search” field at right to see). As for “tosser,” the OED defines it as “A term of contempt or abuse for a person; a ‘jerk,'” and etymologically originates it in the same activity as “wanker.” But it seems to be used rarely if at all in the U.S.
However, “poser” is worth looking into. Here’s what the OED has to say:

Since “poseur,” from the French, is an almost identically-spelled synonym, it’s worth looking at the OED deets:

This suggests to me that “poseur” has been out and about since circa 1870; the Time and Maxim (American lad magazine) citations and a Google Ngram Viewer chart suggest it’s been used with relatively equal frequency in the U.S. and Britain.

The Anglicized “poser” is trickier. First, note all the citations are British. Second, I suggest that the Pall Mall Gazette and Shaw (” The man..is young, agile, a talker, a poser, sharp enough to be capable of anything except honesty or altruistic considerations of any kind”) quotes are interesting outliers, in which the straightforward noun “poser,” one who poses, is extended to the derogatory meaning the word would later come to adopt. Even the 1987 Guardian quote (“I’ve always been a poser,..but the first time I did a modelling job I was shit scared”) seems to refer to literal posing. Only the final quote, from The Sun, sounds like the “poser” one is used to today: “The former World Cup striker is shown as a precious poser who wears a blond wig and refuses to play if it’s raining.”
It’s a little hard to be definitive with “poser,” since in database searches I’ve found it impossible to separate out two other meanings of the word: a hard-to-answer question (“that’s a real poser”) and a French verb meaning to put or to place. But assuming that “poser”=”poseur” had taken hold in the 1980s (by which time “poser”=tough question had fallen out of fashion), Ngram Viewer shows almost twice as frequent use in U.K. as in U.S. (As I’m fond of saying, reliable data for Ngram Viewer only goes up to 2000.)

But the word has caught on on this side of the pond. The main character in a new Broadway play by Tracey Letts says Radiohead’s Thom Yorke is nothing but a “scrubby little poser.” (I know Yorke is English, but Letts is a Yank.) The headline of an ad in the New York Times reads
Getting Digital Right: Posers, Players and Profits
And last month Forbes had:
Peak Performer Vs. Professional Poser: Creating The Right Team
Earlier this year, Times columnist Maureen Dowd wrote that Democratic presidential candidate Beto O’Rourke has been compared to “a middle-school poser who ‘went to Zumiez and spent $27 on stickers.'”
Don’t ask me to explain that. I only come up with the quotes, not what they mean.