Buying a flat in London at 23?

I am 23 and have been in my first job since graduating for around a year and a half, earning 78k with a variable bonus but this year it was 10%. I have been renting in London since my first year of university and am desperate to buy simply to get away from landlords & estate agents! I have had terrible experiences every single year moving and I feel like it's getting worse. I really value a sense of stability and want to live in the same place for a period of time because moving once a year is not good for me.

I am lucky to be in the position to have 80k worth of savings (that is ALL my savings), and my salary means I could get a mortgage of around 350k. Right now my priority is to stay as central as possible as I really love London and I find it hard to imagine ever moving out. My dream place would be a small 2 bed period conversion flat somewhere in Hackney for under 450k as I have my lifetime ISA. I can see a couple of flats that match my requirements on RightMove at the moment, but I am not sure if they have some hidden structural issues or leasehold problems that are making them more affordable. I am also not sure how much to dedicate to a deposit if I were to buy - should I try and use as much of my savings as possible to get my LTV lower, or put some aside as an emergency fund?

I wanted to know what the general consensus was on if it is a good idea or not to buy a place ASAP at my age? I haven't been in my job for too long so if I lose my very inflated salary then a ~400k flat would be unaffordable. My plan would be to rent out the 2nd bedroom for ~800pcm, which would help get my mortgage payment down from around ~2k. For context I currently pay 1k (not incl bills) for a shared room in a flat in central london, saving around 40% of my payslip each month which is about 1.5k. I am desperate to have somewhere long term to live but I don't want to make a stupid financial decision. I can't imagine at this point wanting to live any further out than zone 3, but I am aware as people get older they generally like to live a bit further out. Any opinions would be really useful