Battery-operated Modem

[#1]

I've used battery powered mini-modems on PC's over telephone lines to communicate with remote servers in the 1990's - they were meant to be portable and only for occasional use.

[#2]

@desrosiers 

I’m confused. You say you need a modem. Is this to connect to Plusnet mobile? If so get a Huawei E5577.

If you want to connect to Plusnet broadband presumably if you need a modem then you have a BT landline going to this remote location? If not is it really an access point that you need? If you can get power to within 100m run an Ethernet cable from your router to this remote location  you could use a Power over Ethernet (PoE) Access Point, a google search will give you a choice.

[#3]

Thank you Baldrick1.  Great answer.  Will pass this on to my Ring contact and to PlusNet and see which way to go.