I received a reply from Westminster Archives to my question about the purchase of the diary and it's whereabouts before that.
Here is the reply:
I did contact Miss Swarbrick about the acquisition of the diary and I have heard back from her. Apparently it was she who bought it, not Mr Osborn, although he did the index. Winifred Myers, the vendor, was someone who sold manuscripts, but I was unable to find her listed in the Kelly's Post Office London Directory for 1972. I had wondered whether she might have been another descendant of Nathaniel's, but obviously not. Miss Swarbrick says of the diary "it came with no provenance and was not part of a larger archive". So the mystery of its custodianship between 1846 and 1972 still remains!
So, unfortunately nothing to help us there. I have replied asking if Miss Swarbrick purchased the diary from Miss Myers or from her estate as we discussed a while ago. I suspect the latter.