[Please remove mods! <3]
Best to look into the housing lists in your area as I believe throughout the UK there is currently a huge backlog. As sensible as it may seem to wait until you have funds ready, you may want to get yourself on the list sooner so that you're higher up the list when you are ready. It is a little unclear because some people apparently go on the waiting list with no intention of getting a house, but you may still be waiting a long time for a property. I'm not familiar with the process though so I'm not sure if there are downsides to being on the list earlier.
In terms of advice for being in your own place, I would probably say have a think about what you know and what you don't. It's not to scare you out of it, but to make sure you have a bit of an idea on what to do, and also give you the opportunity to learn things before you move out. There's essential stuff like do you know how to cook, clean, etc. Then admin stuff like sorting utilities, broadband, insurance, etc. And then to knowing what to do when things go wrong or for prevention. What do you do if the electric trips, if there is a water leak, gas leak, fire, carbon monoxide alarm, etc. Do you know where the gas isolators, water valves, mains breakers are? In a council property, a lot of maintenance should generally be done for you, although it often happens very slowly.
Also, just because I have no idea why this isn't checked more often, you can get an electrical tester plug (link) from screwfix for about £8. I recommend buying one and testing every socket. They're really simple, and a constant tone is what you're are after. If it beeps, call the council for an electrician. For some reason they don't seem to include this simple socket test on the survey I had, even though it takes 5 seconds to perform, and a couple of minutes to do the full house. It might be different for council properties as there will be safety standards, but for £8, just test it yourself for peace of mind.
Some of that may sound scary, but a bit of up front prep and knowledge goes a long way. It makes you a bit more prepared and self-sufficient, and means you're not as panicked if something does go wrong because you already have a bit of a plan to use, even if it's just first steps to give you some time to think.
I think I was 15 when I left home. My upbringing was harsh, if not cruel - but mainly due to ignorance rather than vindictiveness if that makes sense. It wasn't actually my choice to leave, but by that time I was so used to their ways that I accepted their actions as normal - just another thing - you could say I was numb and desensitised.
I guess I still had feelings for my Mum at the time - part of me hoped she would change and become the loving, caring person she was never able to be, so I understand it when you talk of your feelings for your Mum despite the way she is treating you.
I could advise that you speak to her, and tell her how you feel - but my heart is telling me that it wont change a thing. In fact you may get on better if you live separately - and she may give you some respect if you are independent too.
Personally, I'd get on and make those plans. Work out what you need and get saving. Possibly keep your plans to yourself - because people have a habit of either talking about it - to the wrong person - or putting you off. Once you get your own place you'll have nobody to answer to but yourself, and that should be liberating - even if it might feel daunting to begin with. I really wish you good luck.