Hi June,
You don't say if you have Joseph Peacock's details from later census, I can give you details from 1851 onwards if you want them.
He wasn't in Great Ayton (Yorkshire) in 1841, so looked for Peacocks in and around Romaldkirk (also Yorkshire!) - there weren't many, in fact only two - this may be him and perhaps his sister, but no sign of his father:
1841 HO107/1247/2 fol.14 p.4 Cotherstone (Romald Kirk parish)
In household of George Pickering, occ. given as Beer House:
Joseph Peacock 18 Ag. Lab born in county
1841 HO107/1247/2 fol.4 p.3 Skein-bank, Cotherstone (Romald Kirk parish)
In household of John Watson farmer:
Margaret Peacock 20 F.S. (female servant) born in county
As later census all have the Peacocks living in Barnard Castle not far from Romaldkirk perhaps the rest of the family is there somewhere in 1841, but it's a big place to search without an address. Please let me know if you need these 1851- later census details
Barbara