Being a Yank, I don't know what the laws and documentary procedures are in the UK.
When I was closing in on putting my car on the road I went to get my car re-registered since it had been off the road for more than 20 years and was titled and previously registered and retitled in another state. When I went to the Department of Motor Vehicles, I told them the VIN was 3635R because I didn't know or had forgotten about the first numbers (7306 - denoting the year and month of manufacture). They didn't know any better so my registration and title says that is my VIN. It isn't actually and I would suspect that the Brit equivalent of the DMV might know that. On the other hand, when your car is identified "on the road", the plaque under the windshield will be how they do it and as you stated, that only has the last 5 characters of the VIN. On a "normal" car, the whole number would be there.
I'd ask the bureaucrat who deals with licensing what you should do.