The following were baptised as children of Henry Thomas Cole & Elizabeth:
Henry Thomas b 29 Oct 1819/bap 28 Jan 1821 - Limehouse St Ann - mariner of Limehouse
Elizabeth 15 Aug 1823/31 Aug 1823 - 182 High St, Corn Dealer - Shadwell St Paul
Elizabeth Jane 14 Apr /26 Jun 1832 - Limehouse, mariner - Limehouse St Ann
John Silas 29 Aug 1830/26 Sept 1830 - Limehouse, mariner - Limehouse St Ann
William 3 Oct 1835/21 Feb 1836 - Salters Place, mariner - St George in The East
Charles Colet 6 Oct 1821/4 Nov 1821 of M.E.O.T., mariner - Stepney St Dunstans & All Saints
Edward James bap 10 Oct 1830 - of Ratcliff, mariner - Stepney St Dunstans &All Saints
Mary Ann - ditto as Edward James.
Elizabeth 1823 doesn't fit or indicates another Henry Thomas Cole. & Elizabeth around at the time.
Three children baptised within a month in 1830? A big gap between first two and the rest?
What makes you sure that your William is Henry Thomas?
Jo