Edinburgh is pretty terrible for shopping. If you're after Cashmere/Wool jumpers one of the shops on the Royal Mile or Rose Street are probably your best bet but they all look like tourist traps so I never go in there. I was home last weekend and the only decent shop in town at the moment is Corniche but it might not have what you're after - Nigel Cabourn, CDG, Pedaled. To be honest, your best bet might be to go in there and ask Ian and Nina for their help, super friendly people. You've got places like Harvey Nichols which have your usual designer stuff although do have some that was pretty good (Pal Zileri, Gieves and Hawkes and some interesting streetwear brands that I hadn't seen up north before).
Actually, Jenners might be a good bet but in general it has gone really downhill since it was taken over by House of Fraser several years back.
Also, and this might be a bit late but won't flying into London Luton be the easiest for getting to Northampton? It's one of these airports that the cheap airlines market as London but isn't really. I know from experience that it's about 30 mins to Milton Keynes and Northampton isn't that much further north from there.