I believe there's County Van Hire that hires out a 3.5 tonne converted van - I've never used them, so can't recommend but I know of people that have and they've never complained.
I know a couple of people who you can pay to transport you in the lancashire area, that come well recommended, but I've not mentioned them as your message makes me think you want to hire the van, rather than a van and driver.
I've hired County Car and Van hire's box many years ago. Its one of those Ifor boxes, so they stand in like they would in a trailer (but wider partitions and there is more storage). I had my 16hISH in with no probs and it was really easy to drive.
I used the County one this summer, very easy to drive and the mare travelled find. The only thing I was a bit wary of was that it has a very high centre of gravity, as it is a trailer body on a transit chasis, but it was fine.
I use horse boxes for hire. It is prestige horse boxes. The 3.5t boxes are all new. I have hired both 3.5 and 7.5 boxes from them and they are very good. Obviously they are well maintained as they are horse box builders by trade.