I agree with Damo, Dave and Scar.

There is no legitimate reason to change the VIN number on a used shell.

Use of a second-hand shell is expressly forbidden under the registration rules, and Plod should have noted the use of a secondhand shell and then DVLA would either allocate a Q plate or may allow the use of the reg number and identity applicable to that shell if you managed to convince them you had actually repaired that car with enough of its own parts (brakes, steering, suspension, etc)

It sounds like, in your case, you have benefitted from a mistake by a cop, but I doubt another one would take your explanation if the ID of the car ever came into doubt.

Anyone looking at a car with a chassis number welded (or pop-rivetted!!!) over another is going to ask "WHY?. Incidentally, the chassis number MUST be stamped into the structure of the car, with a seperate plate attached showing the same number in another location.

Back to the original question - if the shell is brand new it won't have a chassis number from the factory. You contact the Local Vehicle Licencing Office, tell them you have reshelled a car and produce the paperwork and receipts along with the aplication form. They issue a chassis number, and you (or your garage) stamp that in, get the car MOTd, take it for an SVA test - both of which are done by chassis number, not reg number and confirm to LVLO that the number is now stamped in - then they issue a reg number - either the original one, or an age-related one. Or a Q if they are unsatisifed.