Thanks to this excellent website, I am able to add a new Keene-Gillow link:
Firstly, to clarify the family tree, which got strangely altered in transmission, John Keene (c.1775-1842) was the father of William, John, Frederick and James Keene.
As I am now informed, the eldest son, William (born c.1803), married Clara Gillow (born after 1804), 6th daughter of George Gillow of Hammersmith. Thus the Emma Keene I mentioned was indeed the niece of Agnes and Rose Gillow.
Thanks to Keith Gillow for this information. I would still be interested in more general details relating to the Gillow-Keene circle.