I cant find a baptism for David Polhill Green around the 1780's, but possibly matching with the 1803 burial and the children named so far (there was also a Charles Green baptised 4 Apr 1790 at St Mary, Ealing, son of David Polhill Green & Mary), there is this Indenture dated 2nd December 1767:
David Polhill Greene, son of Jonathan Greene late of the parish of St Bottolph without Aldgate, Gentleman, Deceased, doth put himself apprentice to John Cardell, citizen & clothworker of London, to serve from the Day of the Date hereof, until the full End and Term of Seven Years...
This is followed by a memorandum that on Saturday 7th September 1771, the Mayor and Aldermen of the Guildhall of the City of London adjudged that David Polhill Greene be fully discharged from the apprenticeship with John Cardell (who I think had died) and be turned over to someone else to serve the rest of his apprenticeship.
On what looks like the rear of the Indenture it then says "Afterwards to wit on 7th September 1767 And this day by virtue of the Annexed Judgment turned over to Jno Williams Founder of the same trade"
The 1767 must surely be a mistake and should be 1771.. ?
Looking for his father, Jonathan, there is a marriage bond dated 18 Jun 1744 for Jonathan Greene, bachelor of the parish of St Botolph, gentleman, and Elizabeth Cardell spinster.
Added: Oops, didn’t read the second document! Jonathan was 24 & Elizabeth was 21 & upward and from the parish of St Mary, Whitechappel (sic). They intended to marry either at the parish church of St Bennet near Pauls Wharf, St Ann Aldersgate or St Catherine near the Tower Garden.