Could the act of emailing publicly available information be deemed illegal?

[lookingfine]

Suppose the following scenario. Bob and Alice are friends/ex-partners. Bob discovers that Alice is secretly working as an escort. Her activity is legal in the country she currently lives in. Bob tries to convince her that escorting is harmful and will have a serious impact on her mental well-being in the future. Mary disagrees and asserts that her activities are solely relevant to her private life. To stop her, Bob decides to send an anonymous email to her family in which he provides a link to the PUBLIC page she is using to promote her escort services.
Does Bob commit any crime in revealing a PUBLIC website to her family? Could this in particular be considered a cyberstalking crime? What does British law say about this scenario?
I stress that all the information shared by Bob is PUBLIC and visible on the web.
Many thanks

[atticus]

Is this a student question?

[lookingfine]

Is this a student question?

No it is a real case...

[atticus]

Who is Mary?

This could be an offence. I note that Robert and Alice are former partners.