@Elektriksheep 

A very similar topic has been discussed in this forum just recently.

You may have a look here https://community.tp-link.com/en/home/forum/topic/250032.

@woozle Excellent, that's just what I needed.  Thanks.

For others who come across this thread I found this info:

"Well spoke to Vodafone technical support and they said that they don't offer public ip addresses.

So their wifi mobile sims are not suitable for use with game consoles, even though their blurb says they are.

The attraction of the game consoles is the social use and if you cannot, for example find someone to play against on Fifa 16 because the internet service you have has a strict NAT, it is useless.

I did suggest to the technical support that they need to remove this from the adverts.

Well looks like I may try Three as they seem to offer public ip addresses."

Taken from here:
https://forum.vodafone.co.uk/t5/Archive/Public-IP-Address/td-p/2493359

Actually, I seem to have found a solution that doesn't require switching to Three mobile using this information (taken from here:

"The NAT type thing on gaming machines is usually related to the router(s) forwarding certain TCP/UDP ports to the game machine's IP address. However, the MR600 at your home might not be the only device between you and the Internet that is performing NAT (Network Address Translation). Since you are connecting via 4G the first step is to check if Vodafone is assigning a private or a public IP address to your MR600. Log on to the Web interface of your MR600 ( usually via http://tplinkwifi.net ), click on the "globe" pictogram and then check the "IP Address" that is shown a little further down on that page. If that IP address falls within one of the following IP address ranges, then you've got a private IP address, which means there is another NAT on Vodafone's side.

10.0.0.0 – 10.255.255.255
172.16.0.0 – 172.31.255.255
192.168.0.0 – 192.168.255.255

Depending on the result of above check it can then be decided what's the next step towards resolving the NAT type issue."

My router's IP address defaulted to an IP address that falls into the third range of IP addresses listed above and was therefore a private IP address. I have now changed my router's IP (go to network->LAN settings->IP address) to one outside of the above IP address ranges and now my Xbox is reporting Nat type: OPEN!! :D

Edit: My Xbox still reports NAT type; OPEN but the main game I wanted to have an open NAT type for (Call of Duty: Warzone) is itself reporting my NAT type as moderate.  So I'm confused.  Will play the game a bit with this new setup in case it has actually improved the situation.

@Elektriksheep 

Hi,

The post you referred to meant to check whether the IP address of the Internet connection (WAN connection) is public or private.

If you set your router's LAN to a public IP address range (which I didn't even know was possible, since I never tried it ) you probably just trick the detection algorithm of the Xbox into believing it is connected directly to the Internet, but actually it's not and direct incoming connections from other Xbox players will still not come through.

Using a private IP address range for your own router is not a problem, because you have control over it and can setup port forwarding or DMZ as you wish.

However, if your ISP has setup another private network between its customers and the actual Internet (which they do to save precious IPv4 addresses), then you can't do that.