I am more-than-half wondering if this is a joke, actually.
I would tend to think that yes, Canadian and American English are probably a lot closer to each other than either is to British English. But even so, I watch "BBC America" on cable all the time, and almost never have any trouble understanding what is said, except for a few people with very pronounced accents.
In addition to things like truck/Lorry, elevator/lift, flat/apartment there are more subtle things.
For instance, in the US, if you wanted to approach a stranger and ask for directions or something, you might walk up to them and say "excuse me..." then ask your question. Yet from what I've heard, if you do that in England, (say "excuse me") people think you're telling them to get out of your way - which can seem pretty odd if you're on an otherwise empty sidewalk (or "pavement" in the British vernacular.)
Also, in England, what Americans call the "first floor" of a building is the "ground floor", and what Americans call the "second floor" Brits call the "first floor"...