I had some help from Names from Clwyd for Rogers.
1841 Census Wrexham Town
Mount Street. All in same household, no relationships given .
ROGERS
Samuel 72 Breeches maker Not born in County
Frances 65 Not born in County
John 35 Shoemaker Born in County
Thomas 23 -do- Born in County
WHOMSLEY Willm. 30 Whitesmith Born in County
There are some details that match. A Samuel in the marriage , and the ages of Thomas and his brother John who are both shoemakers.
Marriage 2 Dec 1850 St Mary, Birkenhead,
Thomas Beckett Rogers Father's Name Samuel Rogers
Ellen David Thompson Spouse's Father's Name John Thompson
1851 Windle St Helens .Lancashire
Thomas Rodgers 32 shoemaker b Wrexham
Ellen Rodgers 24 b Liverpool
George Rodgers 9 b Wrexham
Samuel Rodgers 7 b Overton
John Rodgers brother 45 shoemaker b Wrexham
There is tree on the User Submitted Genealogies on family search which seems to be this family, just click under Frances Hobson for the children and there is a Thomas and John of similar ages.
There is also a Beckett conection.
https://familysearch.org/ark:/61903/2:2:9MKQ-G8K Queen Street . in household of Sophia JONES 35 Ind. Not born in County
NEWNES Martha 20 Female Servant Not born in County
King Street. in household of Sarah FOULKES 55 Ind. born in County
NEWNES Anne 30 Female Servant Not born in County
There are only these two with the surname NEWNES in Wrexham at this time.