By using a VPN you are essentially routing your internet traffic through another computer and another ISP. So you have one of the VPN provider’s IP addresses. So what they have to do is find out which IP addresses are used by VPNs and block those. It’s very hard, but for the biggest companies somewhat doable.

It depends on what type of VPN you have as well, because if you have one that gives you a dedicated IP, chances are it wouldn’t be detected. But most of your regular cheap VPN packages will have you sharing the same IP as hundreds (thousands?) of others.

BBC iPlayer does this all the time