More evidence it is the correct family I think.
On the '51 John isn't there, but Ann is listed as married not widow.
Ann 50 Head of household
E daughter 21 lace runner
Mary daughter 17 lace runner
R son 14 apprentice shoe maker
Mary Barlow Mother Widow 78 (born 1773)
Thomas Barlow Brother Married 54 Stone Mason
Ann Oram daughter widow 23 pauper
Charles Oram grandson 2
George Oram grandson 0
Martha Butlin grandaughter 7
All living at 156 Crown Yard, Rothwell, Kettering, Northamptonshire, England
Jamjar