Have you seen these - http://www.cera-packaging.com/mug-mailers-p-295.html - I think the brown ones are slightly bigger than the ones at Coralgraph. They're 120mm x 103mm x 90mm.
I haven't tried them myself but came across them yesterday as I have been looking around at the alternatives. It looks like MOQ is 1 pack - 20 boxes. Delivery £7.99.
Might be worth a phone call.