Hi and welcome to Rootschat
As Thomas was born before Civil Registration was introduced
any birth/baptismal records would be on either the IGI at
www.familysearch.org or in local parish records
The 1861 census shows him b Madeley 1836 but there is no IGI entry for his birth. Emma was also b Madeley
In 1861 they had a son Edward aged 3 so I think this may be Thomas with his parents on the 1851 census for Madeley transcribed as Dorrcott
All b Shropshire - children b Brace Meole (Meols?) except George
Corfield Row Madeley
Edward Dorricott 48 bricklayer b Condover
Ann 47 b Sherif Hales
Edward 18
Elizabeth 14
Charles 5
Henry 11
Jane Dorrcott 7
Samuel 10
Thomas 13 George 2 b Madeley Wood
Thomas Haynes 27 lodger