Thank you very much SteveG, SaDgit and Zildjian - immensely useful info!
We have been round in so many circles with this that we're getting motion sickness, but the upshot after consulting with Stephen Whitehart, Heavy Vehicles Process Manager at VOSA Testing and Support Services, is this:
The F250 was never properly classified when it was imported, and as it stands shouldn't even be on the road. It should never have been tested in Class 7, as its GVWR is 3991kg, way over the max for that class. It can't shimmy into Class 4 either because it's not solely a passenger vehicle and does not have 4-wheel drive (so bye-bye to dual purpose or multi-purpose vehicle classification as well).
The fact that it is over ten years old means that we can't use the Individual Vehicle Approval route to change it to an M1 passenger vehicle, which would have dropped it into Class 4. This route, to quote Steve Whitehart, would in any case have been long-winded, expensive and infuriating as it would have apparently brought us into the orbit of many, many nit-pickers who would have delighted in pulling the vehicle metaphorically to pieces to fail it, particularly as US vehicle manufacturers have never produced vehicles that necessarily fit with all the European vehicle regs and standards, and of course this would probably apply even more so to older vehicles like ours.
What we have been advised to do instead is to either email VOSA Technical Officers with all the information, plus pictures, and throw ourselves on their mercy to see what they class the vehicle as - the supervisor I originally spoke to did say that in his opinion and from his long-time instincts, because its load bed was "not used to carry goods or load" but only for our own possessions and equipment (hello demountable camper), it would fit as a Class 4, which has no upper weight limit, but he couldn't guarantee that the Technical Officers would agree with him on that. This process could take quite a long time.
Stephen Whitehart, the Heavy Vehicles Process Manager, on the other hand, said that the vehicle can't legally be on the road with its current GVWR because it's not testable as it's not in any known class at the moment. He also pointed out that the Revenue weight listed on the V5C, which is 2045KG (UNLADEN) is nonsense - the Revenue weight should be the GVWR, ie vehicle weight plus maximum permitted load, which is the weight whereby HMRC calculate how much wear and tear you're going to be putting on the nation's road network and therefore how much tax they should whack on you. This figure should be written on the V5C as "XXXXkg GROSS".
He advised us to voluntarily down-rate the vehicle ourselves. He said DVLA would be loath to approve the change without a Design Weight Certificate, and told us how to get one from him.
We can either get a new door pillar sticker made up, or make one ourselves, with the GVWR reduced from 3991kg to 3500kg, email him a photo of that sticker
in situ on the door pillar, along with the VOSA form VTG10 (Application for Design Weight Certificate) which costs £15, and he will issue us with a Design Weight Certificate showing 3500kg as the GVWR. We then send this certificate with our V5C to the DVLA, who will issue a new V5C showing "3500kg GROSS" as the amended Revenue weight. The pickup can then be tested as a Class 7. Oh happy day.
Hopefully this will be helpful to some other bewildered and bothered owners of large Yank Tanks.
Of course, this leads to a whole other set of problems with removing weight from the camper, but with the air-con, fridge and cooker all being swapped out for lightweight units, I think we'll win with that one fairly easily. Another day, another thread....
