Anything is possible but the cost may be prohibitive.
To put some randomly chosen engine into a G-reg or N-reg CofA plane would cost, at a guess, hundreds of thousands of pounds in paperwork and a huge amount of time.
In the USA you can do it, by reclassifying the plane as "experimental", and this has resulted in some amazing planes with e.g. turbine engines. Here this cannot be done, since the CAA requires (as a revenue maintenance measure) that any plane capable of having a CofA to have a CofA. There are some exceptions where a given type exists on both CofA and Permit.
The UK Permit category and applicable paperwork issues I know nothing about.