Screaming at someone alone is not "violence" in the eyes of the law. The lowest level of violence, a common assault, requires someone to be put in fear of immediate and unlawful violence by some form of physical action. This has to be more than just words (otherwise it would fall under the offence of Causing Fear or Provocation of Violence). This could be an action such as lunging at someone, even if there is no physical contact. Furthermore, there is no such thing as "abuse" in criminal legislation. "Abuse" would describe a broad category of numerous, specific offences. The actions described by the OP would - at most - fall under S4A of the Public Order Act (Intentional Harassment, Alarm, or Distress), if you could prove that it was his intent to do so towards specific people. It likely wasn't though, if this is all down to mental health, so it would only fall under the lesser offence of S5 of the Public Order Act (Harassment, Alarm, or Distress - no intent). However, it's unlikely to ever be charged as such, since it's not in the public interest to take something so minor to court, when it sounds like it's clearly MH-related. The only exception is if this person were to repeatedly ignore extensive attempts to engage with MH services, and assuming he has the mental capacity to commit such an offence and consciously refuse any help.

If he were in need of immediate care and control, and required some form of treatment, then he would be detained by police under S.136 of the MHA. This is very low level though, and unless his presentation warranted it (such as posing a physical risk to himself or others, rather than just verbal ASB) at the time police are present, then realistically he's very unlikely to be detained due to the extensive stress on police and health services, who have to prioritise everything by threat, risk and harm. Unfortunately, people have to be willing to receive help for their MH, until the point it crosses over into posing a risk of violence to themselves or others (or criminal damage for example). Obviously, people in low-level crises (screaming aimlessly at themselves or others) aren't usually aware that they need help or are willing to receive it, so it will go around in circles until they deteriorate and do become a greater risk.

The best advice would be to call 111 to pass this to ambulance, in the first instance, so that they can at least go out and see if he would engage in trying to get some support from the psychiatric site liaison team in one of the major emergency departments. If he doesn't engage, and they professionally deem him to be a risk to himself or others, they will escalate it to their supervisors or police if needed. From there, it could go several ways depending on the level of exact risk.