Living with toxic parents and student loan

I live with toxic parents. My dad is abusive and can be controlling. I am going into my second year of university. I only get a 4k loan from student finance because my dad refused to put his details down. The loan does not cover my accommodation, my accommodation is nearly 6K. He agreed to help me out for university for accommodation, but my issue is there are times where he threatens to not pay for me anymore. If I move out of my parent's house for good, how do I prove this and will I get a higher loan? Also, it's hard getting a job due to coronavirus and I am trying to find a way to increase my income. But my issue is I have a learning difficulty, so I will have to spend more time studying in the library and I am also studying law.

how old are you at the moment? if you're under 25 with no kids and not married then the only way around it is to take a year out and not live with or contact your parents in that time so that you can claim estrangement after that. have you maxed out your student overdraft and could you go for the cheapest accommodation possible?