During the 1850s, Harriet Martineau was carrying on a (brief?) correspondence with my old pal, the evangelical novelist Emily Sarah Holt. Holt was in her late teens at the time, writing rather bad poetry in imitation of Felicia Hemans; I would guess that she's the one who instigated the exchange (fan mail?), unless they had some acquaintances in common. Unfortunately, the VWPL doesn't have the letters in question. *trots off to find the relevant letters*
Incidentally, here's a record of a conference paper on Holt--circa 1883.
(Correspondence discovered while in the course of reading John Warren, "Harriet Martineau and Anti-Catholicism," Recusant History 29.2 (2008): 212.)