Right, I thought it ought to work as well. But although they both seemed to add on successfully in the field where you actually paste them in, the £5 credit from the birthday voucher evaporated from the final total once the other credit voucher was added. I tried a couple of times, it was really odd.
After faffing with it though I just didn't have the energy to contact CS for the sake of a fiver. And now that it's expired, that's an extra layer of complication, so I think I will let this one go. Next year I'll try and deal with it more promptly.