Hi Deni, this have changed since the local DVLA offices have closed as every thing is now done by post!!!
To correctly register your car you'll need to fill-out form V627/1 and include receipts, photos ect.
Personally, I send the completed V627/1, the current V5 (with changes clearly marked) , receipts for the body conversion, a good photo of the car before, during and after the conversion (clearly showing the registration number), plus a photo of the chassis plate number or stamp and engine number.
I also included a new MOT certificate, this proves the car has been built to a road worthy standard, confirms the conversion is completed, confirms the chassis number, confirms the colour change and in most cases the MOT tester will change the VOSA details on his computer i.e. model, colour ect.
.IMHO I think DVLA look upon a MOT test as a form of "independent" inspection.
So it's worth sending a few quid getting an MOT test when your build is ready and before you register it.
Another thing to remember is when fill-out the V627/1 you only give basic simple understandable information and never mention "kit" or "used" or "second hand".
In my recent experience and using the info above the re-registering process takes around 2 weeks from posting the paperwork to receiving the up-dated V5.