The previous post on “Piss off!” mentioned the (originally American) expression “pissed off,” meaning annoyed, angry, etc. There are two British equivalents, “browned off” and “cheesed off,” both of which date to World War II and both of which are NOOBs.
I’ll cover “cheesed off” today. All the citations in Green‘s Dictionary of Slang are from Britain or Commonwealth countries, for example this from a 1946 Philip Larkin letter — “I sympathise very much with your cheesed-off state.”
The earliest U.S. use I found was a 1983 New York Times quote from Congressman Les Aspin, referring to a heated debate about a nuclear freeze: ”Tempers are frayed — the boys are getting cheesed off.” (Interestingly, Aspin was from the American state of Wisconsin, which is known for cheese.) In 2008, in The New Yorker, Hendrik Hertzberg referred to “Hillary [Clinton]-supporting women who are still mightily cheesed off that Obama beat their candidate, despite his comparatively short resumé and so on.”
I got some more recent hits using my new favorite tool: the geo-tagging feature of TweetDeck that allows you to see tweets originating from a particular region. Here’s what came up when I set it for 200 kilometers from New York (Joe Maddon and Gabe Kapler, mentioned in the first tweet, are baseball managers):
Next: “browned off.”
notoneoffbritishisms.com 
In UK, “cheesed off” is more like fed up – “pissed off” is angry. I don’t think the subtleties cross the Atlantic in fact.
True, cheesed off has a different meaning to pissed off. I’ve never heard of browned off.
I think I’ve heard “browned off” (and it’s in Chambers Dictionary) but not for many years. It’s probably a bit old fashioned now.
Although I suppose cheesed off could mean being fed up with an irate nuance. Whereas pissed off is more purely irate.
When I was a kid, I remember my mother would sometimes say she was “cheesed off” with me if I was being naughty. She meant it in an annoyed/fed up kind of way.
I agree with the commenters above. “Cheesed off” is not equivalent to “pissed off” – “cheesed off” means annoyed, rather than angry.
I have maybe seen “browned off” in print a couple of times. I doubt I’ve every heard anyone say it. I know it’s Out There, but it’s not an expression that’s really familiar to me.