Do you get British humour?

I was told a joke last night and I didn't laugh. (Sorry about that!). The joke was:

"What's the difference between a wife and a mistress? - About 30 pounds!"

"That's an American joke", I said.

"How can you tell?"  I was asked.

"Because you can predict the answer from the question," I answered. "Assuming that a middle-aged man, with a middle-aged wife, takes a younger mistress, you can list all the probable differences between the two women. A British person wouldn't laugh, because British jokes typically depend on the question leading you to predict a certain answer, and then the answer is a surprise twist."

To illustrate I told The Chicken Joke:

Qu: "Why did the chicken cross the road?"

The teller of this joke often makes up their own answer, which must be a) original and b) slightly absurd. For instance:

"Because it was the hedgehog's day off"
(ie, that it is the JOB of a particular animal to cross that road each day, and the job happened to fall to the chicken that day)

"Because the pheasant wanted too much money"
(Pheasants, being luxury meat, probably demand higher wages than chickens)

"Because the peacock was too busy posing for photographers"
Peacocks, being beautiful, are probably the celebrities of the bird world)

"Because the kangaroo couldn't get a Green card"
(here the animal who was first offered the job was a foreigner, who then wasn't allowed into the country)

"Because the jellyfish couldn't"
(jellyfish don't have legs, so would be an unsuitable candidate for the job)

"Because the dodo had died"
(they gave the job to an animal from an extinct species)

Because the unicorn.....oh, I expect you get the idea.

This ancient British joke is one of my son's favourites:

"What's black and white and red all over?"
The original answer was a newspaper: printed in black and white (this is an OLD joke) and read (sounds like red) all over. Everyone expects to hear the original answer, so nobody gives it. Unexpected answers include:

a sunburned penguin
an embarrassed panda
A nun swimming in a pot of red paint
A newspaper wrapped round a pound of liver

etc.

The classic British joke, which many foreigners have heard but few see the humour of, can be found in Lewis Carroll's classic children's book, Alice's Adventures in Wonderland. Alice is asked:

"Why is a raven like a writing-desk?"

She can't guess, so she asks what the answer is. But the questioner hasn't got one! Even British people expect a riddle (a joke in the form of a question and "surprise" answer) to actually HAVE an answer. As always, Carroll is a step ahead of his readers.

More examples of British humour would be very welcome! I will add some more when I think of them.