Thank you Trish and BumbleB. I've been trying to recall exactly what I know as opposed to what I surmise. From what I originally received through family connections and from web sources, Phoebe Farnell was the daughter of Martin Farnell, who lived in Coton-in-the-Elms from 1750 to 1815, and Frances Mathews, probably born in Edingale, with Phoebe being born around 1796, though I have no direct evidence for this. Martin seems to have been quite a prominent figure, but at some point seems to have gone bankrupt and it was from his will that I discovered that Phoebe was not actually his daughter, whereas the family thought we were descended from him.
I have the record of the marriage of Martin Farnell to Frances Mathew on 17 march 1805 in Lullington, so the information about Frances seems basically to check out.
Therefore, although Phoebe is listed as Phoebe Farnell at her marriage, she presumably must have been born Phoebe Mathew(s) and assumed the name Farnell after her mother's marriage to Martin.
Mathew(s) was either Frances' married name, in which case there should be a marriage of a Frances someone to a someone Mathew(s) in or around Edingale probably before 1796, or Mathew(s) was her maiden name and Phoebe was illegitimate.
As you correctly point out, Trish, Phoebe seems to have died in 1835 and so is not to be found on any censuses, which would have been a great help otherwise.
Having written all this to get my thoughts clear (and allow anyone to pick holes in my reasoning), I will now go back and look at what you kindly reported!