The person I replied to praised the bobbies for letting them move their party elsewhere. It's entirely possible they went on to disrupt citizens in another part of town. The way London policing works, this sort of thing can go on all night--an "anti-social behaviour crawl." It isn't fair to the people who actually live there.
Partying and anti social behaviour should be dealt with over time with care. Things like dry zones, fines for property owners, police presence and steering the crowd somewhere less impactful.
While not fair for you to deal with, the punishment needs to match the crime. Guns and violence aren't appropriate as per America, fines for property owners could be a solution, and most immediate action such as jail or on the spot fines needs to come after the situation escalates, not on a neighbour's whim.
A word and a written warning is absolutely enough to begin with, if it carries on then start to escalate consequences.
In my experience most people will either leave or tone it down when police show up. Just their presence is usually enough to let you know to keep things reasonable.
In Australia we have some massive fines for things like disturbing the peace, which is why police presence works. 300+ depending on state. But they are not enforced until absolutely nothing else has worked.
or at any times.
Two things that people commonly do in the centre of cities is get drunk and buy drugs. They go to parties, nightclubs, pubs, they make lots of noise. That's the whole point of cities. They are supposed to be grimy, raucous and beautiful.
If you want a good nights sleep, move to the suburbs.
Due to the noise created two or three times a week by junkies who sat down there and got high, I called the police. About once a week around 2 or 3 AM for a few months. I took pictures documenting all the action and gave them to the police. When the police arrived in time to find the screaming drug addicts outside my window, they were just as you describe: incredibly polite, and ineffective. They would ask some questions then leave.
Please think about it from the perspective of the people whose sleep is disrupted night after night after night by substance abusers screaming and drunk people carousing, before we celebrate the kind and gentle bobby.