The APN setting is only not possible with the iD SIM inserted, I can add APNs while using the other SIMs. Apparently, locked routers pop up an unlock menu if you put in a different SIM. I've bought a second B353, the second one is a B535-333 which has an RJ-11 socket for a phone in addition to the 4 RJ-45 LAN sockets. The second router will not arrive before next week so I'll keep investigating the original in the mean time.
All the indications are that the router does not recognise the iD SIM at all. When comparing the iD SIM with the others, the iD SIM has a larger centre section. While it seems unlikely, I'm now wondering if the SIM doesn't make proper contact inside the router. I tried the iD SIM in my Proroute 4G router and it works fine. Apparently I can get another SIM FoC at Currys and may try that next time I'm in town.