Here in the states, I've never heard of that BBC radio show.
I think I could go for a little comfort with a little nostalgia.
A few old country tracks, some classic rock from the late sixties and early seventies, a bit of big-band swing, and one or two quiet instrumental pieces for evenings on the beach.
Johnny Cash - Folsom Prison Blues
Merle Haggard - Silver Wings
The Eagles - Take It Easy
The Allman Brothers - Melissa
Creedence Clearwater Revival - Have You Ever Seen the Rain
Glenn Miller - Moonlight Serenade
Vaughan Williams - The Lark Ascending
Brian Eno - 1/1 (from Music for Airports)
Book ?? ... Robinson Crusoe - Daniel Defoe
Might be some pointers to survival on a desert island in there.
Luxury item:
A good pocket knife. Nothing exotic, just something reliable like a camping knife, I could use for a dozen little jobs every day.
On a desert island, that seems less a luxury and more like sanity in your pocket.
Besides, I'd rather have that luxury item than a device for playing the 8 songs I brought along for some strange reason.
EDIT: For me, any audio recording would be impractical. The environment and ambiance of a desert island would suffice as serenade.