Well, it turned out not to be Whitefriars. Harry Powell's Venetian glass was much lighter in style, the pontil scar was generally ground out and polished, and the stem much slimmer.
Thanks to all at the National who explained it to me.
Patrick's image gives me a date to work around, which is useful.
So, being realistic, we arrive at any one of a number of Stourbridge manufacturers plus two or three others elsewhere like Walsh, with a late Victorian or Edwardian date.
Does anyone have any suggestions for such a piece with a lightly fire-polished neat pontil scar and a merese?