I found your Thomas in the baptism register for Holy Trinity Church Kingston upon Hull. He was christened on 12 Oct 1829 and the register confirms his date of birth as 5 May 1829. His parents are listed as Thomas Havercroft (labourer) and Dinah.
Coincidentally I came across two other children of Thomas and Dinah in the same register. Dinah born 20 July 1826, christened 11 Jan 1827 and Alfred who was christened on 5 Aug 1833 (no date of birth given). I came across these two names, from amongst the hundreds of baptisms carried out annually at this busy church, because they were listed on the same page of the register as ancestors of mine. These were Joseph and Ann Havercroft (both christened 8 Jan 1827) and my great-grandfather John Henry Havercroft christened 7 Aug 1833. This double coincidence does suggest some family link between the parents Thomas and Dinah and my gg grandparents Joseph and Frankey Havercroft.
The Thomas that Colin Havercroft (my recently discovered second cousin) is referring to in his message to you is another son of Joseph and Frankey. He was also born in Kingston upon Hull but on 9 March 1829, two months before your Thomas.
A search for the offspring of Thomas and Dinah on www.familysearch.org lists five children including the sisters Dinah and Betsy (Bessie?)referred to in your letter. No sign of a Frederick though. If their parents were writing from Barnetby le Wold in 1853, the chances are that they will appear on the 1851 census there. If you wish I will have a look next time I do some research in London.