Without un-favouriting all of my current favourites, and then favouriting them again, is there any way to change the order that my favourites appear in?
Unfortunately you can't. However, on the PC version it is possible to assign shortcuts to certain favorite items.
Press Q to bring up the quick menu. Then, hold down a number key (1 trough 8) while hovering over a item or spell for a second. Swap between items during gameplay by tapping the assigned number key.