It was an interesting experience to watch that way. Series 18, the advent of JNT as producer, was a year long transition for the show. JNT changed the tone to reduce the humor so prevalent particularly in the previous series when Douglas Adams was the script editor and wrote three of the stories. By Season 18 Adams was gone from Who, and the broadcast of the TV version of H2G2 coincided with the exit from E-space and the subsequent re-introduction of the Master.
I clearly remember watching H2G2 when it aired on PBS (I believe this was late in 1981) I've been a fan of Adams ever since, and only became aware of his connection with Doctor Who much later.
BTW one of the Adams scripts "City of Death" (well almost totally re-written by him to place the whole story in Paris) presages Clara's story. The "Monster" in that story, Scaroth, had been fragmented into pieces and scattered through time, albeit less pieces than Clara.