That sounds like a story just made up.
If it is a show car / marshall car for racing, I don't think it will be sold on to someone. And chances of that person bringing it over here is slim isn't it?
I actually help Japanese people who come here to work import cars. Stuff like Prelude, Impreza, Altezza are popular.
Get the Vin number off the guy, and get a copy of Japanese document. (De-registration form, or MOT equivalent) I could probably trace the history. You can actually ask Honda to do this too. Check the car too, is the Vin number all in the right places?
Actually, reading your post again, it is unlikely it could be exported without first being on the road in Japan. Nor is it possible to import a car into the UK properly without proper paper work.
Likely scenario is, it was obtained in Japan (stolen, or other reasons - I'll explain it in a sec) Smuggled in a container. Then either ringed (just chassis number attached from a UK car and same number plate as an existing car - so there could be another one in the UK) What is the number plate?
This year alone, I have been offered dodgy NSXs from various dealers in Japan. They varied in prices from 3000 Pounds to 6000 Pounds. All has problems. Not the car, the car is perfect, but there are few situations in Japan where cars could be dodgy. 2 of those cars have been black one. One of them had white leather.
* stolen : obviously
* finance prob : the money lender seized it
* most likely one is, the owner couldn't afford to pay for it anymore, and sold it, then have not returned the money to the lender. This still has finance outstanding, and is technically owned by the money lenders. But cos they can't find the car, they can't find it. But if they did, they will take it off you.
Where is it? I can come and tease them with you!
I am sure it is already done, but make sure the speedo limiter is removed. All Japanese cars are limited electronically to 112 mph.
Speedo should have been done though, in order to register a car that is less than 10 years old you must put it through SVA test. One of the test is speedo calibration. (in MPH)