As we know, in the films' classic continuity, Ernst Stavro Blofeld's rank within SPECTRE was Number 1 and Emilio Largo's was Number 2. Based on this, I think it very likely that members' numbers reflect their rank within SPECTRE. Moreover, it would stand to reason that once a member died, he is replaced by the member directly under him, who thus takes on the deceased's old number.
This allowed me to create a chart of SPECTRE hierarchy per film. Each film column shows the ranks at the beginning of the film, with the symbol † indicating which characters are dead by the end of the film. Characters whose presence in the film is certain are shown in plain text, whereas those whose presence I can only infer from their role in other films are in italics. It is here in PDF:
The number of SPECTRE's inner circle in the novels was 21. That information is not necessarily canon to the film, but, to my surprise, it fits surprisingly well with my calculations' results; the lowest rank I got was Helga Brandt's, who was apparently Number 18 during the events of Doctor No.
I also took the liberty of assigning numbers to two characters whose rank within SPECTRE was not clarified. The first is Dr. No, who, to be in charge of such a large and expensive base (and allowed to propose James Bond with a place within SPECTRE), had to be a member of the Inner Circle, and probably a high-ranking one at that. The second one is Irma Bunt. She is the only other high-ranking SPECTRE agent seen in On Her Majesty's Secret Service, and appears to work in close coordination with Blofeld himself; in the books, she was reporetedly even implied to be Blofeld's mistress, though considering her appearance in the films, I find that somewhat unlikely to be true in that continuity as well. At any rate, all this makes me quite certain that she is actually Blofeld's new Number 2 after Emilio Largo's death.
I also somewhat wanted to find a room for Fiona Volpe in there; she seems to have a similar positiont o Helga Brandt, who was explicitly said to be a numbered SPECTRE member. However, I wasn't sure where to put her. I suppose she could be one of the various question marks left in the chart.