As has been said, very little is currently known about Bermondsey Glass, or its designer, Guy Underwood - at this point it is an assumption that he designed all their glass. A little is written in Cyril Manleys book Decorative Victorian Glass (pages 28,75 and 99) and there is a mention in British Glass Between the Wars (in Appendix IV, under British Tableware Producers 1918 1939, page 111). Both briefly discuss the same two pieces, which, at the time, were the only known examples and BGBtW/Dodsworth concludes "Nothing known about this factory."
Manley notes that both pressed and blown wares were made by the firm (on the basis of the two items he owned). He also notes,
as the two pieces shown are so different, especially their method of manufacture, there must be some exceptional specimens waiting to be discovered. I think Paul has found such examples. I also think that the glass plinths were made and finished especially for these stands - similar to other glass stands have been seen from the 1920's and 30's over the years.
Unfortunately, Manley dates the company to C1900, which would be unlikely with the words British Made written on the base of the known pieces of Bermondsey Glass. If anything it would indicate early 1930s, as Dodsworth suggests in his essay about Gray-stan in BGBtW with the addition of British after Gray-stan; These probably date to the early 1930s when there was a Buy British campaign in operation.
I own three marked items of Bermondsey Glass, two are blown and the third is another version of the pressed, or cast, Madonnas Head that is illustrated in Manley (also in blue glass). Although I have owned two of them for many years the third, a blue cased blown vase is in the 'cloudy' fashion of poor-end Nazeing (possibly even what I now refer to as the Elwell type Nazeing). This stimulated my interest in the subject because of it's similarity to Nazeing examples.
As a result of this interest I have been assembling as much researched material as I can find and have also used an appeal poster on my stand at fairs - so any additional information would be gratefully received (either through this GMB thread or directly to myself) and acknowledged when published.
1930's Nazeing (1934 - 1939), Powell (1928 - 1939), or Gray-stan (1926 - 1936) have a great deal more finesse although it is possible that they might have influenced Bermondseys production. Stylistically, the Bermondsey pieces and the Guy Underwood pieces in this thread owe far more to the late 1920s and the 1930s than to beginning of the twentieth century (pre First World War), so I would challenge the dates of c1900 defined by Manley and c1900-1914 as suggested on Great Glasss website.
At this point in time, there are maybe 9 known and marked pieces of Bermondsey Glass. Until there is a large enough quantity of marked items, it is unlikely that we can say with any accuracy that there are particular characteristics associated with the firm that would allow us to identify unmarked items as from that source, but I suggest that the work dates from between the World Wars.