OK, this seems to be a fair match for the 1881 family above, but Thomas' wife is Elizabeth.
1871RG10; Piece 3088; Folio 53; Page 49 - Feeder Arm (Canal Boat), Harborne, Smethwick, WorcsThomas CARTWRIGHT Head 34 Boat Steerer b. Hanbury, Worcs
Elizabeth CARTWRIGHT Wife 35 b. Droitwich
Hannah CARTWRIGHT Dau 14 b. Droitwich
William CARTWRIGHT Son 8 b. Droitwich
(Possible match for husband of Jane YARNALL?)John CARTWRIGHT Son 4 b. Hanbury
Alfred CARTWRIGHT Son 8 months b. Rickmansworth, Herts
1891RG12; Piece 2343; Folio 42; Page 29 - Hanbury Terrace, Droitwich, WorcsThos. CARTWRIGHT Head 53 Waterman b. Hanbury
Elizth. CARTWRIGHT Wife 56 b. Droitwich (Deaf)
Thos. CARTWRIGHT Son 13 Waterman b. Droitwich
RG12; Piece 2343; Folio 42; Page 30 - Wharf, Hanbury St, Droitwich, WorcsJno. CARTWRIGHT Captain 23 b. Harefield, Middlesex
Jno. BROAD Mate 19 b. Wychbold, Worcs
Ages and birthplaces vary a bit, but this was the only Cartwright family I could see with canal connections. As Charlotte said, John and Mary's marriage cert should give his father's name and occupation, which would confirm whether we're on the right lines.
Do you know when/where Mary Cartwright (who married George Beauchamp) was born? If it was pre-1911, have you found her on the census?