Some of these are guesses. Others are from what I remember reading in liner notes, interviews and Sturdy's book.
'81 Peel Session: Joy Division, Violent Femmes, Artery, Echo and the Bunnymen
It: Leonard Cohen
Freaks etc.: The Birthday Party. Also, is this around the time Jarvis discovered Scott Walker?
Separations: "Pet Shop Boys meets Barry White", disco, new wave, Bowie
From there onward, I kinda think everything just sounds like Pulp. You can hear influences, but everything is alchemized. Nothing is derivative. They pretty much established their identity as something unique, albeit part of the lineage of great British pop and rock.
There are clear Scott Walker influences on a fair few Pulp records i.e. "Freaks" and "Separations". It might also be worth noting that the start of "Rattlesnakes" and the end of "Wickerman" are very similar to two Walker songs ("The Seventh Seal" and "The Electrician").