{The photo does not allow us to read the inscription.}
The photo of the house showing the plaque, c.1920, comes from Plumstead Stories.
Rosemary and Richard Christophers of The Lightbox, previously Woking Museum, have put paid to the rumour that the plaque is held by that museum. They also kindly inquired of Gordon's School whether it is held there, but no, the School don't have it either. This plaque really does seem to be well and truly lost.
Site: General Gordon's birth place - lost plaque, oblong (1 memorial)
SE18, Woolwich Common, 29
The house is long gone. The area is shown on this 1898 map, with the house at the centre, marked as '29'. Before its demolition in 1971-2, the house had boasted, at different times, two plaques commemorating Gordon's birth. See General Gordon's birth place - lost plaque, blue for the other one and for more information about the building.