Just going by the birth years I found a likely family in the 1891, 1901 and 1911 census records.
The 1891 has Thomas and Jessie with four children living at Holt Road, Acton, Wrexham, Denbighshire.
Birth year for Thomas is given as 1854 born Wrexham, Denbighshire occupation painter.
Jessie's birth year is 1862 born in Birmingham.
Registration District is Wrexham
Piece No. is 4614
Folio No. is 15
Page No. is 7
The 1901 has them living at 2 Adpar Street, Paddington, London, Middlesex
Thomas is again a painter/decorator, birth year 1855 and place of birth given as Wales!
Jessie born 1862 Birmingham
They now have eight children with them
Registration District is Paddington
Piece No. is 1
Folio No. is 116
Page No. is 5
In the 1911 they are living at 68 Clarendon Street, Paddington, London
Thomas birth year is 1856 and occupation House Painter. Place of birth has become Wrotham, Derbyshire!
Jessie birth year is 1863 born in Birmingham so she is consistent with her place of birth.
Five children with them. The original image reveals that they had 11 children born, eight still living and three died.
I found most of the birth registrations for the children which suggests that mother's maiden name was HORTON. However when trying to find a Jones/Horton marriage nothing appears.
May mean that they didn't marry, or got missed off the GRO or mis transcribed, or Thomas may have already been married. The children's births are all over the place so difficult to be sure where they married, if they did.
Or Jessie was originally Mary and decided to add Jessie later. There is a possible marriage for a Mary Horton to a Thomas Jones in the SQ 1870 Dudley.
A possible birth as Mary
HORTON, MARY MILLS
GRO Reference: 1862 M Quarter in BIRMINGHAM Volume 06D Page 47
Something for you to mull over for the moment. I may be barking up the wrong tree altogether as you did not mention any names for their children.