hi, I'm a girl who moved from an all girls school to Westminster for sixth form. Honestly I really loved my time there - I'm a big fan of the old buildings and being surrounded by so much history. The location is so central and it's amazing being able to walk past Big Ben and the Houses of Parliament each day but also peaceful and cut off in its own way with Deans Yard and little Deans Yard. It's also really cool when there are special events going on at the abbey (even managed to see King Charles before the coronation!). I think I had it easier joining than some other people did as I had some of my closest friends from my old school who also moved with me and this made settling in and having a good friend group much easier. You will eventually find a friend group though, even if it takes time. I personally really liked all the talks and clubs on offer and the fact that two afternoons a week are devoted to sports.
I don't think there was - or at least didn't notice - any bias towards certain departments during my time there. In terms of what person suits the school most I would say you have to be very academically inclined and motivated. There was quite a lot of work and homework (but this is teacher and subject dependent) and I did humanities rather than stem. I already came from a school where there was quite a competitive academic environment so maybe this didn't impact me as much when I moved to Westminster. It is, however, not a nice place to be struggling academically given that most people are very high achievers. Especially when it comes to uni applications and oxbridge in particular, it can feel very upsetting if you get rejected given that everyone else around you is getting in and talking about it (they had something like 90 oxbridge offers this year).
There is, however, a big mix of people at the school - studious, sporty, sociable, all of the above...I found in general that most people were quite friendly and sociable and I had a good social life while I was there and would often stay at school until late in the evening hanging out with friends, 'working' in the library and sometimes having dinner at school. there are also a decent number of parties. You'll probably find that you're friendly with and chat to a large number of people during your time there even if you have a smaller friendship group. this was the case with me at least.
I don't think that getting in at 16+ affected my university applications - if you're worried about this just make sure you work hard and make a good first impression in the first year - there will be plenty of opportunities to do so through tests, exams , essays etc.
Another point to mention is the Saturday school. I was pretty exhausted throughout my time there as it basically felt like we had a one day weekend which wasn't much of a break. Having said that, it was pretty social as we often went out for lunch after school which was fun.
All in all I really enjoyed my time there and miss it a lot and will always look back on my time there very fondly. It is definitely intense and at times stressful so it just depends on whether you are cut out for this kind of academic environment or are prone to comparing yourself to others etc., but from my personal experience I would definitely recommend it - just depends on what type of person you are.