Really isn't a good plan except for to move. Going through the council or landlord can take months then you will likely get screwed anyway.
LIved here for a year, fantastic, not a peep from any neighbours. New guy moved in upstairs, awful noise from day one, weekly party till 3am or so, noisy friends who like to be drunk and loud in the hallways waking people up. Slamming every door possible, waking me up at all hours, being loud throughout the day screaming off the balcony, etc.
After 4 months they had a full on fight rolling around the floors and throwing each other into walls and doors. Police came, arrested the guy that(afaik) is still there, the other one had basically run away because of this guy and was later found and taken to hospital. Seemingly when the one guy got back he threw a tv, a guitar and some other stuff off the balcony.
On site guy finally enraged, they did some decent damage, needed a door replaced, holes in walls fixed, etc. The main guy who was the only one on the tenancy was seemingly the one beaten up and moved out unofficially the next day, officially he came back and collected his stuff two weeks later, left, ex girlfriend arrived to get her stuff having given a statement against the guy, police called again as he was choking her and took her car keys off her to keep her there.
So on site guy is convinced this guy has been told to move out, may be being given some leeway to find a flat. Rightmove had the flat listed for rent... then that listing disappeared. I got worried, spoke to on site guys, they still think they are moving. Finally after spending about two days calling every hour or so get a reluctant call back from the landlord.... who tells me the guy upstairs signed a new tenancy for 6 months on Jan 1st... 6 weeks after he had signed the on site guys are still waiting for them to move out as was I due to the landlord not bothering to tell anyone.
Landlord utterly screwed me, has now made it very difficult to get rid of this guy within the next 4 and a bit months.
Move out, I hung on WAY to long, landlords will invariably screw you, noise complaints either don't get taken very serious OR take an insane amount of time to get council to do anything or landlord to evict said tenant. Move out and try and find somewhere that limits potential exposure to noisy neighbours.
Due to terrible knees limiting my options significantly I haven't moved out yet, also because I was mistakenly under the impression they'd be out soon, but I'll certainly be taking the next suitable place I can find. Don't be optimistic about letters or complaining, terrible neighbours are a pain to get rid of and most make noise because they couldn't care less about other people and a letter to tell them to shut up won't change that. Easiest, quickest and best option is move out.