As said earlier by @frollic and others you need to configure an exception for that address (or even the whole domain):
/ee-wifi.ee.co.uk/{EE dns server address}
That should go into "DNS Forwards" in "DHCP and DNS":
You should be able to see EE's DNS IP in the System Log.
See also Stubby needs extra Start after Restart of Router - #6 by AndrewZ