Interesting question. Bellamy may cite Rachmaninov, but I don't hear that so much in his music. Basically, his style (with those very heavy, declamatory arpeggios) sounds more like Brahms or one of the other mid-Romantics. It's written that way so that the piano sounds clearly against loud accompaniment: in Brahms's case, an orchestra, in Bellamy's a rock band.
I think that if you're going to try to get into classical music off that specific sound, you've got a long, maybe disappointing route in front of you. Try some of Rick Wakeman's piano stuff first (he was very influenced IMHO by Beethoven's piano writing) and then try some piano concertos: Brahms, Tchaikovsky, Rachmaninov (it can't hurt: they're very good) and - for an unusual one - try Busoni's as well.
If it's solo piano that you're looking for, try Beethoven's "Hammerklavier" piano sonata, but it might still be "too classical". Alternatively, Busoni's "Fantasia Contrappuntistica" is a good example of very heavy Romantic solo writing, as would be Liszt's Mephisto waltzes. Whether Bellamy could actually play any of these pieces is another question ...
