I have the following from Michael Gadd, an Underhill Family researcher:

Quite probably, Sarah is the daughter of Joseph Underhill and his wife Sarah Smith who appear in the 1841census for Fillongley, Warwickshire, England.
Surname First name(s) Sex Age Occupation Where Born Remarks
UNDERHILL Joseph M 70 Farmer Warwickshire
SMITH Sarah F 40 Housekeeper Warwickshire
UNDERHILL Mary Ann F 12 Warwickshire
UNDERHILL Eleanor F 10 Warwickshire
UNDERHILL Maria F 6 Warwickshire
UNDERHILL Joseph M 5 Warwickshire
BURTONWOOD Sarah F 15 Female Servant Warwickshire

Joseph was buried at Fillongley on 16th June 1849 aged 83 and Sarah appears on the 1851 Census at Big House, Fillongley, as Sarah Underhill, age 52, with her younger children Ellen, 21, Maria, 16, and Joseph, 14. So, whilst at the 1841 census return, Sarah appeared as his housekeeper, I suspect she was more than that.

The IGI christenings show that Joseph & Sarah had at least 6 children
together:
John Underhill Smith 26th Oct 1821 - buried 23rd May 1840 age 18
Sarah Smith 20th Dec 1821
Mary Anne Underhill Smith 15th Mar 1829
Elianor Smith 14th Jan 1831
Maria Smith 31st Jan 1835
Joseph Smith 16th April 1836

From the transcript they appear to be recorded as the children of Joseph (no
surname) and Sarah Smith.