Another good option is to use something similar to Smart DNS Proxy to bypass geo-blocking by UK (and other) TV channels. I've been using it for years with no issues. There is some configuration involved, but it's not too complicated. You may also have to change you system clock to a UK timezone for the BBC, since they sometimes check for that. I wouldn't recommend using their DNS service for any other purpose though, since there are no privacy guarantees.

IMO most VPNs simply can't keep up with their IP addresses being quickly blocked by UK TV websites, so they are very hit and miss for that particular use case. Plus it's not their necessarily their core business, so they don't put so much effort into circumventing geoblocking. You might find one that will work, but it will often be blocked in a few days or weeks. But your mileage may vary & you may get lucky.