In the 1901 census, the William you found is 40 year old!
Reference RG13, Piece 4758, Folio 120, Page 37
64 & 66 Camperdown Street, Gateshead
Lawson, William Head M 40 Tramway Labourer b Alnwick, Northumberland
Lawson, Emily Wife F 42 n b Gateshead
Lawson, Theresa Daughter F 19 General Servant (Domestic) b Gateshead
Lawson, Emily Daughter F 15 General Servant (Domestic) b Gateshead
Lawson, Willie Son M 12 b Gateshead
Lawson, John Son M 14 b Gateshead
Lawson, Annie Daughter F 10 b Gateshead
Lawson, Edward Son M 6 b Gateshead
Lawson, Robert Son M 2 b Gateshead
Trow, James Lodger M 23 General Labourer b Essex
Nugent, James Father-in-Law Widower M 72 Generl Labourer b Ireland
That still puts his age 10 years out, but closer to 1871!
