If you have reason to doubt whether a person has a licence you can call Licensing and Training Standards and give the details of the individual and they will give you a simple answer Yes or No. Clearly you will need to identify the person, if you don't have a reference number you need the full name, address or location, possibly age as there may be several people with the same name. They cannot tell you anything about the person other than to confirm if there is a licence held that matches the details given. This has nothing to do with the licence verification process. They may not be able to identify if the licence is currently valid as this information is not held on the licensing database.
I understand the seriousness of someone operating without a licence; they may even be carrying passengers!! But, if for example you had suspicions about me and you made a call to the CAA as a concerned aviator and they confirmed I did/did not have a licence this would constitute a breach of data protection policies.
Surely an conversation along the lines of; " Hello CAA I have concerns that Pilot X is flying around without a licence, can you help?" CAA: "I have just checked his details and although I cannot say one way or another, you have nothing to worry about." or "I have just checked his details and although I cannot say one way or another please be assured we will look into this."
I would imagine the correct way to go (although probably extreme) is get the police to look into it, even then they would have to send in a data subject access form if they were to get any answer in writing. Maybe this is moot as I think the CAA would have jurisdiction over such prosecutions?
In FAA land, the pilot must be made aware that his license status will be made public and by accepting such license he is agreeing to this by default? I would be very surprised if we all have agreed somewhere along the lines to the CAA disclosing our licence status to anybody by telephone no matter how serious the potential offense is?