I've recently tried the tutorial from Holly Hopper for an antler headband but struggled with narrow bands that I had available. Does anyone know of a reliable supplier for the bands, preferably the 1" (or 2cm) ones.

Have you tried the search button? I typed hair bands and got this that I posted a while back, there might be more if you try

hair bands, hair band, head band etc

 hair-bands-t9454.html?hilit=hair bands

I'll have a look, cheers.