Bronwyn,
For the 1851 census, the city of Newcastle is covered by five census districts...
All Saints
Byker,
St Andrew's
St Nicholas' and
Westgate.
Available for each, is a Surname Index, from which can be ascertained the appropriate name, age, and census page reference number. Then if census pages are available, it is an easy matter to navigate to the approriate page and gather the required info.
Right then.... the only William Williamson in those five Newcastle Indexes, that came anywhere your target was...
Census 1851 Sandgate*, Newcastle.
Ref Piece 2407 Folio 680 Page 35.
Head William Marr, 24 yrs,violin maker,born Newcastle(N/C)
Wife Hannah Marr, 21, b.N/C
Son John Marr, 2, b.N/C
Servant Elizabeth Williamson unmarried, 24, General Servant, b.N/C.
William Williamson, 2, b N/C
* Sandgate is area at Newcastle Quayside.
Michael Dixon
Blyth, Northumberland.