I recently got a copy of "Are You Being Served?" by Richard Webber, David Croft and Jeremy Lloyd (Orion Books, 1998).
The book tells the history of the famous BBC sitcom set in Grace Brothers' department store, and its sequel, "Grace and Favour".
There is quite a long section on Arthur English, with a few photos, and also a photo and short biography of Brenda Cowling (Lady Caroline Beck in FF), who appeared as a shop customer in one episode of AYBS.
It mentions that both actors appeared in FF but doesn't say anything else about the series.