Why have the decade's most popular movies been saturated with Englishness? Check out the list. A few thoughts:
1. England has a thriving theatre scene that produces many well-trained actors, far out of proportion to its population relative to the USA.
2. An easy way to make a character seem classy or intelligent to an American audience is to give him an English accent. (British English may also be more globally comprehensible than any other accent or dialect, save perhaps American English; yay empire.)
3. England has a different relationship to fantasy literature than does the USA: it is more mainstream there and often on the adult bestseller lists. There is thus a lot of English-language fantasy with a British flavor (and it's orders of magnitude easier to get something adapted if it's already in English). Add to this that blockbuster special effects movies have taken off in the last 10-20 years and that fantasy books were extremely difficult to film prior to the recent advances in FX. Result: there is a giant backlog of British fantasy to adapt. (This is the same dynamic that we have seen with comic book movies.)
4. Pirates are cool. The draw is not in any way related to Englishness. It is merely an accident (through the filming of Treasure Island) that pirates speak with Cornish accents.
5. Titanic: I guarantee that even if there had been no English passengers or crew, they still would have made this movie and it would have looked the same; it's not as if there weren't plenty of sumptuously wealthy Americans.
6. Shrek: the only reason the title character has a Scottish accent is because Mike Myers's father was Scottish and he used him as the inspiration for the father in So I Married An Axe Murderer and for other, later characters, all of which are buffoonish or grotesque. Because Britishness comes off as classier (see 2.a), the apparent contrast between our expectations and the character's behavior is heightened. Would Fat Bastard have been funny with a flat Midwestern accent? Probably not (assuming he was funny at all).