Those loss categories have no legal standing - they are just used by insurance companies to categorize salvage. Its possible to put a CAT B back on the road, infact a quick Google earlier suggests that Adrien Flux will even insure it for you. Its the fact that most companies wont insure CAT B cars that keeps them off the road.
https://www.adrianflux.co.uk/category-b-insurance/#:~:text=Category%20B%20write%2Doffs%20represent,re%2Dappear%20on%20the%20roads.&text=Even%20if%20you%20want%20to,insurance%20providers%20refusing%20you%20cover.
Also if i roll my pride and joy into a ball and never go through the insurance it won't be recorded and I can quite happily repair it and put it back on the road without even needing an MOT!
but, the subject of the original post is changing a vehicles identity which most certainly is illegal.
https://www.adrianflux.co.uk/category-b-insurance/#:~:text=Category%20B%20write%2Doffs%20represent,re%2Dappear%20on%20the%20roads.&text=Even%20if%20you%20want%20to,insurance%20providers%20refusing%20you%20cover.
Also if i roll my pride and joy into a ball and never go through the insurance it won't be recorded and I can quite happily repair it and put it back on the road without even needing an MOT!
but, the subject of the original post is changing a vehicles identity which most certainly is illegal.