Hi Norman, welcome to Rootschat.
Since my original post two years ago I've discovered much more about Florence, working with jmzcollins who posted above (we're half second cousins) and another of her descendants who lives in Australia.
The children that Florence had with my great-grandfather were all registered with his surname of Bowdler, with her name of Brooks given as the mother's maiden name. As per my original post, they were: Peter William Oliver (Oct 1923, Cardiff), twins Patrick and Gordon (born and sadly died 1925, Cardiff); Marion (born 1926, Cardiff); Ruth (born 1927, Okehampton Devon, died 1928 same place); and Kenneth (born & died 1929, Okehampton, Devon).
Florence and Oliver William were never married to each other: he was still married to my great-grandmother (who was in a mental hospital) and she was still married to her husband, John Ralph Hamilton. Florence and her husband had a daughter before she met my great-grandfather - Marjorie Hamilton, born in Cardiff in 1919.
Florence died in 1930 in Devon. While the newspaper reports of the funeral refer to the death of "Mrs O.W. Bowdler" her death certificate records her as Florence Hamilton. My great-grandfather was the informant.
The names, dates and location of Cardiff from your story certainly overlap with that of Florence, but I'm not sure that your father Peter would have been her son. As far as my research goes she originated from Devon, and married her husband John Ralph Hamilton in 1916 in Devonport, then moved to Cardiff. There is no known link between Florence and the Forest of Dean - it is my great-grandfather Oliver William Bowdler whose roots are there.
I've looked at births for a child named Peter Brooks in Cardiff between 1920 and 1924. Aside from Peter W.O.Brooks already mentioned above, born October 1923, the only other record is a Peter Brooks born Apr-Jun quarter 1923. Given there's only a maximum of six months between the two births they must have been born to different mothers.
I hope this helps!