How "new" are we talking? Do you mean brand new bands who have just started or just anything from the "modern era" (90's and 2000's, I guess)
My reccomendations-
Radiohead's early albums, mainly The Bends(has a very 60's feel to it, although it's a bit heavier since it was from the grunge era) and Ok Computer (regularly gets compared to Pink Floyd and Sgt. Pepper era Beatles)
Blur's "trilogy" of albums from 93-95 have a very classic British feel to them, much like The Kinks in the late 60's
Arcade Fire has a wide array of influences; people like The Beatles and Beach Boys as well as "classic" U2 and REM
Beck's Sea Change album is quite different from his other work and has a very country/folk rock tone
There were tons of new bands in the 2000's that drew from late 70's post-punk/new wave bands. The Strokes, The White Stripes, The Arctic Monkeys, Franz Ferdinand, and the Yeah Yeah Yeahs to name a few
Don't know if that was what you were looking for, but there you go.