I tried removing the Technicolor router from the network, and put the BEFSX41 back on and the extenders all happily reconnected.
I am at the end of my network knowledge, but it appears to me that the Technicolor is preventing the connection somehow: Maybe the intrusion detection which I cannot see how to disable?
Any ideas? I tried to put the Technicolor in bridge mode but could not get it to work with my BEFSX41, however I would prefer to resolve this (if possible) without introducing additional equipment.