Got them! It looks as if it is the right James and Ann in 1841
1851. Gwyn St, Bedford St Paul
Ann Smith head widow 62 proprietor of houses b Kempston
William Smith son unmarr 28 currier b Eversholt
Elizabeth Smith dau unm 22 b Eversholt
Ann Bermick/Berwick/Barwick? grand dau 4 b Crawley Beds*
The 1810 marriage I found on the other board (James Smith of Eversholt and Ann Chalton/Charlton) was at Kempston
You really need that 1845 will, which if you're lucky might name all his children
David
* One of the problems of using two message boards is that vital snippets of information get missed. Rereading your query on the other board, I see it reads "My 3 x great grandmother Emma SMITH was born ca 1816, the daughter of James SMITH, in Eversholt according to the 1851 and 1861 census. In 1841 she was living in Woburn, marrying James BERWICK later that year and then lived in Husborne Crawley" So Ann Berwick granddaughter 4 b (Husborne) Crawley in 1851 provides the link between her mother Emma, and her grandparents James & Ann Smith, and ties it all up very neatly.
"Emma did use Ann as the name of her eldest daughter (my great grandmother)." - as Ann wasn't with her mother in 1851 I'm a bit surprised that you hadn't looked for her elsewhere in Beds - she's the only Ann Berwick in the county, for once indexed correctly by Ancestry. This nut didn't need the sledgehammer treatment that it's had!