Some things you could check out:-
the will of Hugh Welch Cooper 1875 who could be a sibling/cousin
I found a Hugh Welsh Cooper in the 1851 census, residing at 479 Oxford street, Bloomsbury. Hugh was born circa 1799 in Dorsetshire, and at the time, was a licensed victualler. Also residing with hime was daughter Eliza J, aged 26, born Middlesex, along with a boarder and 4 servants. Although Hugh states she was married, his wife does not appear on that page.
According to the 1861 census, Hugh is still at 479 Oxford Street, a tavern keeper, and his birth place is now recorded as Bridport, Dorsetshire. His wife, Eliza is now present, and she was born circa 1808 at Langport, Somersetshire. At this time, there are 2 lodgers, 3 servants and a cook also in residence.
In the 1871 census, Hugh (transcribed as Hugh N) is now at Lime Tree Villa, Hammersmith along with a new wife, Emily A who was born circa 1819 at Southampton, Hampshire and one servant. The birthplace is still consistent with Bridport and Hugh has no occupation.
Hugh apparently dies on 25 February 1875, and his probate was proved on 23 March 1875. The probate calendar gives the address for Lime Trees Villa as Gold-Hawk-road, Shepherd's Bush, and the estate was proved by Benjamin Perkins of Gold-Hawk-road and Emily Ann Cooper, widow, two of the executors.
On further investigation, Hugh can be found in the 1841 census at Wakefield street, St Pancras, Mary-le-bone, with wife Elizabeth, daughter Elizabeth, son John and daughter Susan and one Rebecca Pennels. All birth places, with the exception of Rebecca, are down as Middlesex. Hugh records his occupation as builder.
According to Pallot's baptismal index, there was a baptism for a son John Welsh Cooper at St Pancras in 1825 with parents Hugh Welsh Cooper and Elizabeth. On searching further, a John Webb* Cooper was baptised at St Pancras parish church on 15 November 1825 to a High Welsh Cooper and Elizabeth. The register gives additional information; John was born 23 October 1825, the family was at Joseph street, and that Hugh was a bricklayer. [* Image is actually Welsh]
Baptism of Elizabeth Jane Cooper occurred at St Pancras, Old Pancras on 21 November 1823. Elizabeth was born 25 October 1823, and residence was given as Joseph Street. Hugh was still a bricklayer.
Mary Badcock Cooper was baptised at St Pancras to parents Hugh and Elizabeth Cooper on 20 February 1828. The register confirms Mary as being born 27 January 1828 with father Hugh being a bricklayer of Joseph Street.
Another child, Susan Cooper, was baptised at St Pancras Old, St Pancras on 4 November 1830. Hugh is now a builder of Regent Place, and Susan was born 13 October 1830.
A Hugh Wilck** Cooper weds one Elizabeth Babcock on 28 April 1822 at Westminster St Martin in the Fields by banns. No additional information can be gleaned from the Bishop transcript; am unable to read the witnesses' names. [* Image is actually Welsh]
A marriage was registered in July-September 1866 quarter at Strand, London for a Hugh W Cooper and Emily A Hamblett.
Hugh was baptised on 15 April 1798 at Bridport, Dorsetshire to father John and mother Elizabeth.
There is also a Hugh Cooper, along with a Susanna Cooper, buried at Bridport on 23 February 1795. By the naming of Hugh's children, these may be connected.