There are Elthams in Malling / Peckam distict of Kent at around that time - but not as far as I know connected to my Berks / Oxon family. i can't find this Ann on censuses but she may have married an Eltham after 1871. My theory is she was the wife of Thomas Eltham.
In 1871 Thomas Eltham age 62 (widower) is living in Hale street, East Peckham, his unmarried sister Elizabeth is his housekeeper. In Q4 1873 there is a marriage for a Thomas Eltham vol 2a page 812. However the index gives no other people with that page number in that quarter in Malling district. Looking at all the Anns who married in that quarter in Malling, there is an Ann Gower page ref 842. That page reference only has two other people (not three) one male (James Fermer) and one female (Esther Newman). In 1881 census there is a James Fermer and wife Esther living in East Peckam, So it looks like Ann Gower is the "spare" in tha quarter and Thomas Eltham's page reference has been mis-indexed.
In 1871 there is an Ann Gower age 61, the wife of John Gower age 68 living in East Peckham. There is a death for a John Gower age 68 registered in Malling district in Q3 1871. I can't find the death of an Ann Gower of the right age in Malling or neighbouring districts. So the evidence points to this Ann Eltham who died in Malling district being the widowed Ann Gower who married Thomas Eltham in 1873 and died as Ann Eltham in 1879.