There are many, many vampire short stories, and I have read a lot of them, but I'm pretty sure I will name this unhestitatingly as my favourite whenever I am asked in the future.

You make a good argument for it! It was not the first story of Aickman's I read, because that was either "The Stains" or "The Swords," but Cold Hand in Mine was my real introduction to his work.

Have you seen the short film of The Cicerones (2002)? It is actually what started me reading Aickman as an adult.