Hi, within your router settings have you assigned your Xbox 360 to Xbox Live.
You can find out if you switch on your Xbox and find your MAC address.
In the Xbox Dashboard, go to My Xbox and open System Settings.
Select Network Settings, Configure Network.
On the Additional Settings tab, select Advanced Settings, then select Alternate MAC Address.
If you're connected to your network with an Ethernet cable, write down the 12 letters and numbers under Wired MAC Address.
If your using the Wireless Plusnet Router - TG585 v7
Then using your PC go to your Plusnet Router IP http://192.168.1.254
enter username as admin
and your password will be your routers Serial Number, found under your router.
Click Toolbox > Game & Application Sharing and at the bottom click > Assign a game or application to a local network device.
Select Xbox Live
from the Game or Application drop down, then from the Device drop down select the MAC of your Xbox 360 and click Add.
Turn your Xbox off and restart and give that a shot. Apologies if your tried this already. If this doesn't help I will help you get your Xbox outside your DMZ.