So the city, Aylesmouth, was built by a old Ventrue ('noble bloodline') with too much money (as they all have) . It is based on an artificial island, and was marketted as a way to draw people to the UK when eveyrone was following the American dream, marketed as a 'city of the future. On the surface it seems like that, well designed etc, but as there always are, imperfection hide in the parts no-one is meant to see.
On the vampire side it was meant as a haven for old vampires and ventrue to be able to get into the foundations of the new business etc starting up, and provide a place free from the anarchs, and those who are starting to rattle the status quo.
As a way to form a coterie, I had a though that - One way to cement this is while clans were allowed to create new fledglings when granted by the prince, it was done in groups and they were placed in coteries. Supposedly to strengthen one another, but also the coterie were responsible for each other. If one member of a coterie steps out, all are punished. This was meant to make sure they policed themselves, and stopped any stepping out of line.
While that prince is missing, the tradition remains.
Alternatively Kholods suggestion also works, you guys have found over the past year or so working together its easier to navigate the new world you've been thrust into with one another, especilaly when the older vampires see younger ones as disposable, scapegoats and the ones who do all the dirty work. As yeah it starts you all off knowing and getting along to a degree, while the above scenario would likely start with you guys being formed into a coeterie for the first time. So up to you guys really.
If you guys wanna discuss while I get set up, gonna quickly say that for now for story reasons only allowed clans (Kinda like your 'species' are - Gangrel, Brujah, Ventrue, Tremere, Toreodour, Nosferatu, Malkavian, and possibly Banu Haqim. (Assamite)
What I'll try and set up first is things like Clans, and a glossary etc. (Though if you have a copy of rulebook it has a decent one), as World of Darkness loves its fancy words.
I will say don't be put off by not knowing lore etc. New vampires are rarely told more than they need to know, so its perfectly fine to learn in real time alongside your character.