The creator and writer of That's Love! (with Jimmy Mulville and Diana Hardcastle), Terence Frisby (who also wrote the David Jason vehicle Lucky Fellow ten years before), seems to be in possesion of all the episodes of it, as he has uploaded them all on his YT channel.
https://www.youtube.com/@TerenceFrisby1
(It is not clear whether it "officially" exists in archives, and even if they do, it is unlikely it will ever be seen by "legit" manners ever again, as it is in Rights Hell and is unclearable]. :( )
Nice one, I've never heard of it but it's going in my archive for sure.