Query about driving licence address?

Basically, my stepson spends almost all his time in London, and rents furnished flats on short term leases so he moves usually at least once a year. Would it be legal for him to put our address as his home address on his driving licence so that he wouldn't have to go to the trouble of sending to the DVLA for a new one every few months? I can't see a problem as travellers must put an address on their licenses which they must rarely reside at. Anyone with real knowledge of this and not just guesswork please help.