You've obviously studied this, but having actually lived in a city center police sirens are actually fairly rare. Despite what you say they rarely sound them at night unless they really have a need, at least in Nottingham.

Much worse for causing often unexpected and very grating noise were:

1. Bin men, especially now they collect glass

2. Diesel black cabs having to put their foot down to get up a hill

3. Taxis idling outside your window waiting for a pickup or just waiting for their next dispatch on double yellows in middle of night

4. Scaffolding being put up or taken down. Incredibly noisy, actually has to be done fairly regularly, many companies illegally do this at the weekend in the early morning as it's a part time job for them

5. Skateboarders, one of the most anti-social hobbies for everyone else around them [1]

I lived on a bit of a hill, which caused 2 and attracted 5.

Since moving to a village again my sleep quality improved overnight. I didn't realize quite how badly it was affecting me.

[1] As it seems to be causing confusion, the anti-social behaviour is against non-skateboarders "Environmental antisocial behaviour is when a person’s actions affect the wider environment, such as public spaces or buildings." https://www.met.police.uk/advice/advice-and-information/asb/...