I believe he was in Cheshire in 1841, in the township of Tranmere in the civil parish of Bebbington.
John Barnett, 44, Mariner, not born in county
Mary 44, not
Thomas 22, painter, not
John, 14, not
William 12 yes (still with them in 1851)
Mary 6, yes
They must have left Wales before 1829
From IGI: Thomas Hyland Barnett christened 17 Nov 1818 Hubberston, Pembs.
Other children (not mentioned above):
Samuel John, 1822
Matilda Maria Hyland 1823
Samuel 1825
John 1827
All Hubberston
Again, from IGI, William is William Hyland Barnett.
I'd put money on John married Mary Hyland.