Your ISP needs to give you multiple addresses, which the vast majority of residential providers do not.
Using a VPN might be an option, depends if the betting site in question rejects connections from known VPN providers.
This is the problem, they know your using a VPN and close your account.
They would not be able to do this with a "good" VPN implementation. As long as you aren't stupid and go into and out of your account on and off the VPN quickly there is no reason they should think you aren't entering from a perfectly legitimate location. Even better if you can find a decent UK based one. Maybe not going with a "big" VPN provider would help as their IP's may be tagged to them. Think smaller like, good friend with some slack bandwidth?
The problem is they're starting to deny all traffic from IP addresses originating from datacentres.
The only way to slow this down is to have the reverseDNS similar to what is displayed for a residential ISP but even then they'll catch on eventually or just look at route objects.
So a good friend with a pi sat behind his router would be ideal then. Residential ISP with residential endpoint. No problems at all (although I wouldn't let a friend VPN into my network).
Remote desktop/TeamViewer to partners computer on their home network. Job done.
The tricky bit is finding an isp that doesn't charge the earth for it.
Do Zen still offer multiple IP addresses? I seem to remember a while ago they used to offer 8 static IP addresses. What routers can utilize this, a lot of standard off the shelf kit will only manage basic one IP connections.
Edgerouter does PPPoE and supports multiple wan ips and its <100 quid, no?