I believe the situation is no different in Scotland but certainly in England and Wales a “Breach of the Peace” can occur in both public and private places. There is no distinction.
Breach of the Peace is not a statutory offence and is covered by common law. A police constable can arrest a person if he believes a breach of the peace has taken place or is likely to take place. Prosecutions for the offence do not take place. Instead the miscreant is brought before a court to be “bound over” to keep the peace in future. (This does not result in a criminal conviction).
If you say you have been charged with breach of the peace I am surprised. I did not think there was any difference in Scottish Law, but perhaps another AB-er with knowledge of Scottish Law may be able to help.
I note you describe the prosecution as malicious. What makes you say this? Remember, there is a difference between a malicious prosecution and one where you simply do not believe you are guilty.