There not Obscure in the U.K., but bands such as Family, The Strawbs, Slade, The Divine Comedy, King Crimson, and Roxy Music only have a cult following in the states.

What other bands from the U.K. are popular there, but not here?

for more recent examples, I love a lot of Britpop music so it's easy to compile a list, haha

Oasis were popular here in the mid-90's, but it's nothing compared to their ongoing popularity in England. People have compared them to The Beatles there.
Suede
Blur (a few hits here, but massive there)
Girls Aloud (girl group who is nothing here, but major there)
Sugababes (see Girls Aloud)
Shayne Ward (think Justin Timberlake, but British)
Robbie Williams (minor US success, but in the UK, is the biggest solo male artist since Michael Jackson)
The Verve (a one hit wonder in America, revered rock gods in England)
Will Young (think Clay Aiken, but actually cute and actually out of the closet, lol)
Westlife (they had one hit here, but in the UK, they have a record for #1's, that's why Mariah collaborated with them, since they were a way to give her a UK #1 hit, lol)

and plenty others

MIKABOMB- Composed of Japanese expatriots living in London; they met and formed in the UK and thus melded the Osaka girl punk sound, (a la Shonen Knife) with the traditional UK punk genre

going back to the 60s/70s,

incredible string band
bill fay
the pretty things
kaleidoscope
comus
pentangle

actually, i'm not sure exactly how known they are over in the uk, but i know that they're obscure here. by the way, mr. cleveland, i love your signature.

New Wave Of British Heavy Metal (the ones you may not have heard of):

Angel Witch

Tygers Of Pan Tang (featured John Sykes on guitar, who later went on to perform with Whitesnake and Thin Lizzy)

Samson (featured "Bruce Bruce" Dickinson, who later fronted Iron Maiden)

Diamond Head (originally did "Am I Evil", later covered by Metallica. Lars Ulrich toured with them around England in 1980)

Saxon (very popular still, performed "Denim And Leather" and "Princess Of the Night")

Girlschool (performed "Play Dirty", member Kelly Johnson passed away last year)

Sweet Savage

Demon

Tank

Venom (one of the most notorious--and notoriously bad bands from England, album 'Black Metal' from 1982 inspired the genre of the same name)

Grim Reaper (who can forget 1984's "See You In Hell"??)

Raven (drummer Wacko! wore athlete's uniform and pads and pounded drums with his face wearing a hockey faceguard; the band was signed to a major label on the same night as Metallica and Anthrax at the same show in 1983)

Witchfinder General

There is McFly too, an all boy band, consisting of Danny Jones, Tom Fletcher, Dougie Poynter, and Harry Judd.