BBC could ID a VPN IP address based on usage and concurrent sessions, but honestly most companies that block VPNs just purchase IP address lists from any number of vendors. Pixalate and DoubleVerify are two that I’ve worked with in the past that both provide that data to clients. They rarely ever block entire IP blocks though, so you might just try reconnecting from a different location/server within the UK until you land on one that works (if any).