No, it's not illegal to do so when it involves material in breach of the 2006 Terrorism Act. It is reasonable behaviour for groups to take their own action against behaviour that can bring them into disrepute.
Whether it's the marching body or organisers, they do not require permission from the peelers in order to express their own distaste and dissatisfaction with pro-terrorist material.
After that, they and/or organisers can report to the police officers in attendance.
Furthermore, civilians absolutely "can make an arrest if the suspect is actually committing the offence or if you reasonably suspect them of committing it, or when the offence has been committed and you reasonably suspect them of having committed it."
Let's not pretend otherwise.
So, if it is merely a minority doing it, then the majority of the marching body should have no qualms about taking immediate action. 🤷♂️