Margaret,
As has been said, Nelson was a Vice Admiral of the White (Squadron) when he died. (The RN had Red, White and Blue Squadrons until 1864, Red being the senior, Blue the junior.)
This is therefore a comparatively junior flag rank and is actually right in the middle of the Admiral's list. As I see it, Nelson would have had to achieve just one more rank before he became a full Admiral of the White, but an additional three before he became Admiral of the Red, the senior squadron. From Vice admiral of the White, the steps were: Admiral of the White, Rear admiral of the Red, Vice Admiral of the Red, Admiral of the Red. (I seem to remember that the position of Admiral of the Red was only introduced in 1805.) On occasion I believe admirals could miss a rank (although I stand to be corrected) and besides promotion for individuals, there were also general promotions. There were also, of course, several holders of the each rank!
I'm not sure there was a precedent for promotion after death, I have not heard of it (and I see that Brian has just answered this one), but in any case, I would have thought that rank promotions and the awarding of medals are surely not the same thing.
Margaret, Re: the sacophagus, does it actually matter that much that it was not especially designed for Nelson but, I believe for Cardinal Wolsey? In a way, it is nice that a use was actually found for it! In these cash-strapped times, I'm not sure either that the news would go down too well. Who would pay for it?
Mark, there you are, all you need to do is to get to know the Dean!

I remember I was quite surprised when you mentioned before the fact that Nelson was in the basement, rather than on the top floor!

I can endorse what Anna said about the CD, it's absolutely beautiful, with the exact wording and music from the event. Colin White also makes a contribution! I found it best to listen to it in a darkened room.