It is tempting to see a possible connection between this Charles and another group of Thetfords who lived in the St Giles without Cripplegate area of London. This family were the descendants of Dusgate Thetford, sawyer, himself a probable son of Robert Thetford, gent., of Cockley Cley, Norfolk (d. 1679) by Mary Dusgate, and a cadet of the gentry family of Thetford of Hevingham, Sporle and King’s Lynn. Details of this family are in vol. 4 of my study of the Thetford family in Great Britain (available at www.booty.freeserve.co.uk)
To confirm or disprove all this, we need the details of the baptisms you refer to. As far as I know there are no male-line descendants of this branch of the Thetford family, and until I read your note I was not aware of anyone claiming a connection.