אפיקורס עוויקטעד פון האגער'ס שוהל אין לונדון דורך שומרים ארג

I need some legal advice please:

I have been banned from entering a chareidi synagogue in Golders Green after expressing my religious beliefs on its premises. The synagogue members felt threatened by their children's exposure to different ideas, and the rabbi called Shomrim ( the chareidi community police) to physically evict me, which they did.
As a social experiment (inspired by Danny Shine, social experimentalist [look him up on YouTube]) I contacted the police, who told me that the rabbi had the right to evict me as this was his private property.
The question is, is this legally correct? Does a synagogue have the status of a private property, from which the "owner" can evict whomever they wants? Or does it have the status of a public area, in which case they have no right to ban me without proving that I am disturbing social order?

Back to the story, I really enjoyed tonight's encounter with people. I saw the ugly side of people, and the good side of people. The commotion that I caused by being nothing more than myself, showed me how powerful one human being can be when acting with respect and dignity but with confidence and conviction. People who would otherwise wish that they never encountered anyone with different beliefs to them, had to swallow my polite, but firm decline to leave the area. After making sure that I was on public ground, I explained to them that I take their words as a request, but that in a public space they cannot tell me what to do, although they might not like me or what I am doing.
[I cannot recommend strongly enough for whomever has not yet come across Dani Shine on YouTube, to look up his channel Social Experimentalist (which can be found here: <a class="postlink" href="https://www.youtube.com/user/spiritualentertainer&#41;">https://www.youtube.com/user/spiritualentertainer&#41;</a>.]

Whoever has any info on the legal aspect of the matter, please let me know, so I can have some fun.⁠⁠⁠⁠