It doesn't matter whose business it is, the BBC still can't use communication between you and the BBC to interfere in a relationship you have with your employer that is illegal.
If it's somebody posting from home in their own time, dobbing them in seems a bit weird. How do they know who I work for?
I don't know what the status of private communications with the BBC would be in this regard, but if you're using their platform to publish, then I think that my argument holds.
However, if the publisher you sent the book to publishs it, then goes to your boss with the intent of getting you in trouble and/or fired, you might have something to sue over.
Think of it like this: If I'm a web developer and I haven't received payment for my services I can withhold those services or even retain control of the product I am providing or use the courts to enforce the contract, but if I used the client's credit card info to enforce fines and pay myself I have broken the law regardless of whether I put it in the contract.
Otherwise the BBC would quickly find that when they are late paying the contractors who work on their website their credit cards mysteriously get charged for the services rendered.