First off I’ll caveat everything I’m about to say with, if you’re unhappy and want to live somewhere else and would rather be up north, that is completely fine, you should go where you feel at home and happy when you’re able to get out of your contract/find a job somewhere else etc.
However. I’ve lived in London nearly 8 years and no I don’t feel as you do - honestly it’s the only place I’ve ever felt truly at home and I’ve lived in the midlands, Leeds and Manchester. For the first 2-3 years here though, it was about finding out which elements of London worked for me, and finding friends, whether that was through work, hobbies, online. One of my favourite things about London is how every borough/area is a like different little town with its own centre and atmosphere. I’ve not experienced the unfriendliness you mention - where I live now in south east, I chat with local shopkeepers, I’m in a WhatsApp group with my neighbours and we go to the pub together and people do stop on the street to chat (having a dog helps). I also volunteer with a local initiative to help the homeless. Similarly in my last flat in Tooting I found people generally friendly and welcoming in terms of locals, neighbours etc.
I do think living in Brent is part of your problem. Not all house shares are full of antisocial people who don’t come out of their rooms - I house shared for 6 years in a few different places before I got my own flat and I had a multitude of experiences from flatmates who’d have dinner and barbecues together to the kind of unfriendly ones you describe - part of it is luck. I would recommend reconsidering house sharing and look at places a bit nearer than Brent with more of a cafe culture and nightlife.
There are also Facebook groups for people in your position - London New Girl and London Lonely Girls are for women who feel just like you do. I joined them a while ago and have made some friends, people also post house sharing opportunities on there too.
All that said, I did feel lonely at times in my first 3ish years here - it’s easy to feel like you’re isolated from all the fun stuff if you don’t have the kind of friends you can go and do things with, but for me it really did come with time, and now I can’t imagine living anywhere else.