Advising schools on banning a parent from a school site is always difficult. It's difficult because the relationship between the parent and the school is key for educational success and no school ever wants to have to be in the position where it has to consider a ban. However, schools have a duty to consider the well being of their students, staff and other visitors to a school site and as such it is important to know that this is an option.
The Department for Education has provided guidance on this titled "Advice on school security: Access to, and barring of individuals from, school premises." While the guidance is clear that a ban is a draconian measure, it does make it clear that "a school may consider that aggressive, abusive or insulting behaviour, or language from a parent presents a risk to staff or pupils. It is enough for a member of staff or a pupil to feel threatened. In such a circumstance, schools have a power in common law to bar the parent from the premises." It's important to keep in mind that when exercising this power a school should act reasonably (give reasons for its decision), rationally (have regard to relevant factors such as the guidance) and in a procedurally fair way (give people a chance to have their say). In extreme cases bans can be immediate but should be reviewed in light of any representations a parent makes.
It's also important to consider what a parent may do next. Some parents threaten to take legal action by way of a judicial review. So long as a ban has been done in a reasonable, rational and procedurally fair way (and this can be proved) the risk of any successful legal action is low.
Sometimes in connection with a threat of legal action parents may make subject access requests. Because of this, it's really important (as always) that staff be very careful about saying anything in e-mails about a parent.
What is more common is that a complaint can be made. If this happens, the complaint should be dealt with in the usual way in accordance with policy.
Some times a parent may engage in hostile social media activity. If this happens, then it is important to seek specialist advice as there are a range of options to deal with this.
Banning a parent should always be an option of last resort but, at the same time, students and staff are entitled to work in an environment without feeling threatened. But when exercising this power it's important to do so in a fair and reasonable way.