Dave Plowman wrote:

I've assigned static addresses to the things I want to talk to one
another, including the range extender, below 64. And reserved those IP
addresses in the router.

When you say "reserved" do you mean you've set an exclusion for
addresses xx.yy.zz.1 to .64 in the router's DHCP scope, or do you mean
you've associated every item's MAC address to the IP address you want it
to have? The latter is what I meant, then you don't have to give the
individual equipment static addresses, you can leave them on automatic
and the router will look up their MAC and always give them the same IP addr.

You've not said what model BT router you have, then people can check if
the router can do that.

Googled lots of times. Everyone has a different answer.
None of which seems to have made any difference. Some can see another, but
not the other way. Some show another on the network, but aren't allowed
access.

"see" at what level? ping is the starting point, you might need to
enable it through firewalls, once everything can ping everything else,
move up to SMB/CIFS sharing. If you try to use file shares first it's
running before the network can walk.