Census Entry

6 June 1841West Rudham NFK (HO107/771/21 f8 p11)
Name Age of Rank, Profession
or Occupation
Born in NFK?
Harriett BARRETT 40IndYes
William BARRETT12  Yes
Charlotte BARRETT 10 Yes
Sarah BARRETT 8 Yes
Phebe BARRETT 5 Yes
Mary BARRETT 65IndYes
William BARRETT25 CarpenterYes
Sarah BARRETT 25 Yes
Isaac BARRETT6  Yes
Martha BARRETT 4 Yes
William BARRETT3  Yes
Jane BARRETT 1 Yes

The first household is Harriet Barrett (possibly widowed, although I cannot find a death record for her husband John Barrett), and 4 of her children.

The family next door might be unrelated, despite the shared surname.

The 1851 census shows Mary as head, Sarah as her daughter, and William (born Narborough NFK) as her son-in-law. A possible family reconstruction is:-

William's Ancestral File Record 16X2-RL9 refers to the marriage of William Barritt and Sarah Barrett, 26 November 1835 at West Rudham. (Further search gives Sarah's parents as William Barrett and Mary Youngs. Further evidence of the different spellings of Barr[ei]tt can be seen from their daughter Emma's Birth Certificate.)

The IGI lists William Barritt as the son of Richard Barritt and Jane Couch, baptised Narborough 2 February 1811, and also lists his brother John, born 9 September 1805. It is tempting to see this John as a good candidate for John Barrett, the husband of Harriett. However, John Barritt born Narborough can be traced through the census records: such as the 1861 census of Soham CAM (RG9/1035 f112 p23) which lists him with his wife Mary and family. Further, the 1841 census of Northwold NFK (HO107/774/11 f36 p9) implies John and Mary were already married in 1841.