As far as RVW is concerned they've recently played "17 Come Sunday" from the Folk Song suite, 49th Parallel, Rhosymedre from the Welsh hymn tune preludes and the Fantasia on a Theme by Thomas Tallis. At least with the last, its impossible to be selective and chop it into bleeding chunks!
If I want to listen to a particular broadcast work in whole, I'll listen to Radio 3. Apart from the ad breaks Classic FM is ok in that its good background sound and discounting the "popular film and game" music, there is a reasonable spread in the Hall of Fame playlist. Of course that allows them to dip into the H0F to select other works by composers voted for by listeners.
Its not perfect, but its better than its competitors at the easy listening end of classical music broadcasting.