As Sandy points out: just because the vehicle has a tax disk, and the owner has a piece of paper relating to the insurance, this doesn't actually help us: MOTs are done electronically, and insurance can be voided after the paper has been sent.
An MOT test really only certifies a vehicles as being up to a standard ON THAT DAY, one could put on all the bits that make the 90 pass an MOT for one day, and then swap back to the tyres that stick 4" beyond the bodywork; the home-made winch-bumper with sharp edges; the straight-through exhaust; and open up the fuel-pump again (who cares about black reek.... it's behind you!!)
Insurance is only valid for as long as the car has an MOT, for as long as you & the vehicle match the description held by the insurance company (do they know about the after-market side-steps?), and up until the time you try to claim on the insurance (where-upon the insurance company could look for every excuse for not paying :innocent look: )
For an organisation to check the [road] legality of a vehicle, they need a connection into the VOSA database, and that just ain't gonna happen from the middle of a muddy field, on a wet november morning, on a Sunday.
.... and, anyway - does YOUR insurance cover you when driving off the public highway?
(I pay extra on my insurance so that I'm covered when setting up events & officiating at events.... but that took time to get sorted)