Could this be the Josiah COLE who is living in Stanley Road with wife Eliza and daughter Harriet in the 1861 census of Fulham, Middlesex in the 1841 census of Fulham? He is living at Colehill Lane in the household of Richard STEEL, a Market Gardener & his wife Harriet plus various STEEL children but also 3 COLE children, Ellen aged 12, Josiah aged 10 & Nelson aged 6. Josiah Smith COLE was baptised at St Luke Chelsea on 19 June 1831, son of Samuel & Harriot COLE, Old Brompton, Gardener and Nelson John COLE was baptised on 24 May 1835 at All Saints, Fulham, son of Samuel & Harriet COLE, Colehill Lane, Gardener. So did Richard STEEL perhaps marry Harriet COLE the widow of Samuel? But it would seem to definitely rule out this Josiah COLE as being the son of Josiah COLE of Chatteris. Just found a banns record where the banns were read at St Martin in the Fields on 22 & 29 December 1839 and 5 January 1840 between Richard STEEL & Harriet COLE.
Janet