Eqiutrec do but about 50 miles from you 3-5 ton box £130 a day inc insurance, (3 dealers to hire from in Scotland). Elite horsebox hire in Lothians, and Aberdeenshire horsebox hire both do 3-5 ton boxes. Google horsebox hire near Edinburgh.
Not much help because I can't remember the name of the company but there's a new 3.5t hire company just started in fife/stirling/Edinburgh area and they are advertising on FB. It's not a self drive though, the hire includes the driver.
ETA it's Neigh Bother on facebook and it's £75 + mileage, full day shared hire including driver/groom but must be within stirling/denny/plean area so guessing of no use at all to you, sorry!