Originally Posted by Not Anumber
If it is done after the car has been IVA'd and registered it should just be a case of notifying the DVLA of a change of engine number and capacity as with any other car.
If you have not yet put the car through IVA though it may be worth changing the engine details on the donor vehicle's V5 before going through the IVA process. If you do this take a picture of the engine in the donor just in case it is asked for at IVA to prove that engine really was in the donor car.
This is a lot more of a pain than it used to be, the DVLA wants prrof of the engine's origin! or at the least an inspection of the engine number and casting code.