Is this another TV detector van? https://en.wikipedia.org/wiki/TV_detector_van
You can compare to other privacy policies, and note the somewhat ironic fact that other privacy policies are quite woolly and vague about whom personal information will be disclosed to for the purposes of protecting the site, protecting its users, and enforcing terms and conditions of service. For all users know, these companies and organizations could be disclosing it to some randomly selected stranger in a faraway country. The U.K. Information Commissioner has some guidelines for privacy policies, and making it clear what sort of people personal information will be disclosed to is actually a good thing, even though the BBC has been somewhat inept about it.
* https://ico.org.uk/for-organisations/guide-to-data-protectio...
Rather than the vague "we may disclose information" of Apple, Reddit, and their ilk, the BBC is trying to point out that the people that it may disclose information to are going to be the people discoverable from things like looking up one's IP addresses, which is going to include employers if one posts to the BBC site from company computers, schools if one does so from school computers, and so forth.