The Channel Islands are
not part of the United Kingdom, nor are they part of the European Union. They are independent "Crown Dependencies." The U.K. is responsible for their defense but little else.
The islands fall into two "bailiwicks," or jurisdictions: Jersey and Guernsey. The latter includes some of the smaller islands, including Alderney and Sark. Each has its own local laws, its own tax system, and its own money (although the latter is still pounds and pence on a 1:1 exchange rate and Sterling notes and coins are readily accepted).
Many things are cheaper on the islands due to there being lower duties and no VAT. I haven't been to Jersey since 1991, but at that time gasoline was about half the U.K. price, for example.
The Channel Islands fell to the Nazis in 1940 and are the only British territory to be occupied during WWII. Although there have been accusations of collaboration over the years, there are also many stories of how brave islanders thwarted the occupying army.
If you are in Jersey, there is a "Museum of the Occupation" in St. Helier which is well worth a visit (I assume it is still there, as I said I haven't been there since '91).
Some more background information here:
Channel IslandsCrown Dependency