We have experience resolving such issues.
This is a complex and time-consuming process, but it can be resolved. The key is to ensure all homologation requirements are met and a complete set of registration documents are provided.
We've described the specifics of submitting vehicle registration documents in detail
here.
We scheduled the car for an MOT inspection. They checked the steering play, brake effectiveness, headlight performance, exhaust system, engine number (DFA code), and VIN.
After the inspection, we submitted the registration documents. We had to request some documents from the seller. The negotiations and waiting took time.