Okay, so I have a Vigor 2830n router set up with a Huawei E35333 USB 4G modem. It's connecting to the internet just fine, but I can't then dial INTO the router from outside. I've got a no-ip dynamic dns set up, and the IP is being refreshed when the router is restarted, but I can't even ping the public IP that I apparently have. So, is it actually even possible to dial into the router or a suitably configured device connected to it in this fashion? And if so then what else needs to be done?

Does your router actually have a public routable IP address? The WAN address it gets from
the cellco might be NATted/CGN - in which case dynanic DNS won't help. What range is it in?

the ip I get starts 213.205.

That looks like a public IP address so should work. check if ping from Itnernet/WAN is
disabled. Presumably you've tried pinging the IP address too, not just the dns name,
and you're doing it from outside the network ?

I think Admin is pointing out the right thing here:

The majority of (UK) mobile operators (including fixed wireless access like Relish) use CGNAT (Carrier Grade Network Address Translation), so even though you see a public IP when you go to say whatsmyip.org, it is possible that this is double-natted to conserve address space.
Unfortunately, this means only outbound traffic is supported.

Best way to find out is using a traceroute. If you trace to your 'fixed line' connection, and you see an extra hop between your private IP and the 213.x.x.x address you say, CGNAT is applied.