Another candidate for your pieces? They bear a striking resemblance to those of Frederic Griffith trading as H Griffith & Sons. They were a firm of manufacturing jewellers who at that time traded from 131 Warstone Lane, Birmingham and some time later later from Tachbrook Road, Leamington Spa.
My reference for Hugh Green suggested a Liverpool manufacturer who assayed in Birminghan, Sheffield and London at around this date. But I can't confirm this.
However, there are certainly thimbles on the internet with an identical mark attributed to H Griffith & Sons!