The first time I watched this, I remember laughing almost continually and thinking it was comedic genius. All these years later, my opinion's changed fairly drastically. While the jokes are indeed quite funny and Atkinson's slapstick humour is certainly up to par, the same type of joke is used for almost every joke for the entire movie. Basically, Johnny English says something overconfident and suave (ex. "I'm always careful.") and then messes up in a way that's related to what he just said (ex. hitting his head on something). It's funny, but it gets a bit old, and it's really predictable. In terms of plot, this is really simple and totally exaggerated, which is fun but doesn't allow the viewer to properly invest in the story, and we are forced to just kind of observe from a distance.
I'd still recommend this to fans of Mr. Bean or Atkinson; you'll certainly have fun. It's just not anything more than that.
In a sentence:
Well-executed but repetitive humour and a really basic and over-the-top story make this a fun but unremarkable movie.