His occupation in 1901 & 1911 is Gardener, and in 1891 he appears to be at Salem Street, Bishopwearmouth, boarding with a family named Robson – RG12/4139/29/52
Thomas Proud 37 Single Gardener b Sunderland
1881 he is with parents John & Elizabeth plus various siblings at Mill Farm, Durham Road, Bishopwearmouth – RG11/4993/66/58
1871 at Red House, Bishop Wearmouth with parents & siblings – RG10/5006/27/47
1861 at at Proud Farm, Tunstall Road, Bishopwearmouth - RG9/3772/59/19
Based on the later children, Elizabeth's maiden name appears to be ORAM, but I can't find a Proud/Oram birth registration for Thomas, and there is a gap between Thomas's birth (1854) and the next child Robert William (1858).
John Proud married Elizabeth Oram in 1857, so Thomas's birth was prior to this marriage. John was also about 12 years older than Elizabeth, so the unknown is currently whether Thomas was John's son, or Elizabeth's.