I've been having some Twitter conversation with @Lynneguist @BrianAGarner and @StanCarey about whether another usage started as AmE. Have you noticed that (younger?) people say things like "That was a mistake / good move on my behalf" when they mean "on my part"? I think it is now so widespread that "on my part" would sound old-fashioned or even weird to many people.
Someone else on Twitter then suggested that if you are really posh you don't have to do anything at all: you have servants to do everything on your behalf.
A test for many of these points might be "What would they say on Downton Abbey"? Oh, no, on second thoughts ... maybe I'll ask Lisa on " The Real Housewives of Beverly Hills"?