You're welcome, Angus2k18.
I couldn't find an obit for him on the British Newspaper Archive, either, but that might be because they don't have newspapers for the area in which he died.
Perhaps it might be a good idea to contact the libraries and/or local genealogy group(s) in the area where that Alexander died in 1877, just in case they have an indexed list of BMDs or obits.
If none of those pan out, another option would be to start tracing the parents and siblings of that particular Alexander. Perhaps Alexander and his wife might have been witnesses to a relative's marriage or baptism, or perhaps he, his wife or children were named in a relative's will. That's a harder slog but sometimes, when all else fails, it can pay off.
Re. Jane/Isabella: I don't know if the following is relevant but I'm sharing it as an example of confusion over names in records.
My great-grandmother was named Isabella Grace. That's what she was called on her birth, marriage and death records. She was called Isabella Grace in the 1901, 1911 and 1921 censuses, all taken after she married my great-grandfather (the latter after they emigrated to Canada). But she seemed to be missing from the earlier census records and I couldn't figure out why.
I knew who Isabella's parents and siblings were, and they were all listed together in 1871, 1881 and 1891 but, instead of Isabella, there was a child of the right age named Jane. It was only with the help of Rootschatters that I was able to determine that it was the right family and that, for some unknown reason, Isabella was called Jane by her family, at least where the census was concerned. (I ruled Jane out as another child or a twin for Isabella.)
Good luck in your search!
Regards,
Josephine