Could this be your Thomas Bateman, he is also in the 1901 census in Dalton in Furness, England.

1881 census.
Henry BATEMAN Head M Male 41 Lones ?, Isle of Man, England Iron Ore Miner
Hannah BATEMAN Wife M Female 37 Lones ?, Isle of Man, England
Lawrence H. BATEMAN Son U Male 15 Lones ?, Isle of Man, England Ironmonger
Joseph H. BATEMAN Son Male 12 Lones ?, Isle of Man, England Scholar
Hannah BATEMAN Daur Female 10 Lones ?, Isle of Man, England Scholar
Elenor C. BATEMAN Daur Female 7 Dalton, Lancashire, England Scholar
Jemima BATEMAN Daur Female 5 Dalton, Lancashire, England Scholar
Sarah J. BATEMAN Daur Female 3 Dalton, Lancashire, England
Thomas D. BATEMAN Son Male 2 Lonon, Isle of Man, England

1901 - Dalton in Furness
Thomas - age 22
Bessie - 7months
Charles - age 3
Jemima - age 25
Joseph - age 32
Lawrence - age 35
Lucy - age 6
Margaret - age 30
Sarah - age 23

Copies of the 1901 census can be purchased, the 1881 census is on familysearch.org