Re: All the best music was written before 1988 anyway
Likewise WRT John Peel.
But 6Music's evening and weekend programming does a similar job (daytime less so), particular favourites being The Freak Zone, Freak Zone Playlist, Don Letts, Tom Ravenscroft (AKA Peel Jr), Iggy Pop, Now Playing, Cerys Matthews, Guy Garvey, plus the 6Music Recommends shows.
Interestingly (though predictably in the light of other posts here), a lot of the more interesting stuff comes through Bandcamp and Soundcloud, as well as a myriad independent labels. I find it really helpful to be constantly exposed to stuff I haven't heard, new and old.