It turns out that the problem is an address lookup plugin on the Account form.
This is trying to access http://crm:1999
, which is a 404, and http://crm:5555
, which isn't allowed.
Solutions are to fix the server on http://crm:1999
and set up proper managed internal and external URLs so it'll know whether http://crm:5555
or http://crm.ourcompany.co.uk:5555
or remove the plugin.