I moved out about 10 years younger than you are now. I was in the same position about not having much money and so on. Whilst we're an incredibly close family, I didn't feel "grown up" until I had moved out and was living my own life, and whilst I was paying my parents a fair contribution, and doing my fair share of housework and so on, I personally didn't feel comfortable living there as a young virile male either

.
So London wasn't the best place to find a place to rent, but I managed it, in fact I moved in with some gym mates, which was great for a few years - then I saved up enough and started to earn enough to rent by myself.
Sure some people may suggest that it is paying someone else's mortgage, but you know what? I had a home. I had somewhere to call mine and yes it wasn't
mine but in terms of life it was. I never looked back.
Moving out did me lots of good. Now, I'm no Casanova by any stretch, but neither am I a shy recluse, so it certainly helped in terms of relationships. I also felt more independence and freedom, and you learn a lot about being an adult having to fend for yourself.
I suggest you move out as soon as possible.