No encryption...
exploiting the fact that the antiquated technology behind the UK's remaining pager deployments sends messages without any encryption at all.
So, he is picking up unencrypted messages on the public airwaves? I think it is the NHS Trust that should be in hot water! It isn't too bright of the radio operator to stream the results, but it is clearly the Trust that is at fault here.
It is, however, a criminal offence under both the Wireless Telegraphy Act 2006 and the Snoopers' Charter (aka the Investigatory Powers Act 2016, or IPA) to eavesdrop on messages that are not intended either for the public or for you personally.
As they are unencrypted, it could be argued that the messages are being broadcast in the public domain and he is simply a listener. If they weren't meant to be evesdropped by the public, they would be encrypted.
The webcam side is another matter, of course.