Pres Obama referred to "demagoging" in his interview on the Today programme this morning - I haven't looked it up but surely there's no verb 'to demagogue'?
Well, I've just looked it up and not only is such a verb in fairly widespread use, but according to the OED Online, it dates back to at least 1656 (in the sense of "to play the demagogue"). It has been used as a transitive verb, meaning "to deal with (a matter) after the fashion of a demagogue", since at least 1890.
The OED does say "chiefly US", but then Obama is the US president so I'll let him off.
Regarding 'demagoging', Google suggests that 'demagoguing' is the more widely used spelling (32,000 results as opposed to just over 4,000).
And rather bizarrely, searching Google for "to demagogue" with results limited to "pages from the UK" brings up something called JD's World as the first result. Nothing to do with me, I promise...