I have a friend who is currently in England and is waiting until current restrictions allow him to return to Thailand. This could possibly take months.

He has a car out here that he wishes to sell and has found a buyer. He has the book for the car with him in the UK.

How can he overcome the problem of getting the name in the book officially transferred to the the new owner.

You will have to help him if he trusts you. 

He will have to send you the book and a copy of his passport and copy of the page where he was stamped out of Thailand. 

Before that you have to send him 2 papers from the DLT office for him to sign on the part marked X. 

Then the buyer can proceed at the DLT with you and give you the dosh to put in his a/c or if the buyer has his Thai bank a/c No. buyer can pay directly into that. 

Absolutely no chance , if his last Visa for Thailand has expired by more than 30 days. They just wont transfer it without him being here , if the Visa has expired , tried it many times.