Humour is very different all over the world. When you said "English humour", did you specifically mean "the humour used in England, the country", or "humour in the English language (from any English-speaking nation)"?
Some English humour is different from Scottish humour and from Welsh humour and from Irish humour and from American humour etc etc. Of course, there are some things which are just funny all over the world or all over one country.
The British use a lot of sarcasm. Historically, we also used slapstick a lot (personally, I don't find it at all funny).
In the UK, we have some stereotypical views of other nations' sense of humour. For example, many Brits think the Germans use a lot of "toilet humour", that the French have no sense of humour, that Americans use very obvious joke-type humour, that the Irish are just generally funny people with an instantly amusing accent, that Scottish comedians swear a lot, and many other assumptions.
Humour in anything other than one's native language is generally very difficult to grasp. One of my friends has lived in Spain for over ten years and speaks and understands Spanish perfectly. However, he still doesn't enjoy going to comedy clubs, or to see stand-up comedians because he can't really grasp the nuances and frequently wonders why all the Spaniards are laughing!