im sixteen and i want to move out but how?

hi. so brief back story I'm 16 years old and I want to move out of my home with m mother. I've come to the point where I no longer feel I can stay at home and I want to be free from the metaphoric chins I'm tied to, but I have no idea what to do or where to start. Recently a friend has moved into a bed-sit where he pays £15 a week, I myself have tried finding similar accommodation but have not been fortunate in any of my searches and my findings prove to be useless to hopeless. I have no idea where to start and with no contact with this friend because I dropped my phone down the toilet, and unaided by parental guidance I am stuck in what to do, however it is something I have been thinking of for while now and am positive it is something I want to do, I've contemplated and explored all my options and have come to the conclusion its what I need and want. Please help me? I really have no idea where to start or what to do an I need to sort this out

You can either talk to:
1. Social services who are obliged to assist.

2. Shelter
http://england.shelter.org.uk/get_advice/young_people_leaving_home_and_finding_a_place/leaving_in_a_hurry

3. CAB

https://www.citizensadvice.org.uk/about-us/how-we-provide-advice/advice/search-for-your-local-citizens-advice/

They can tell you about benefits and give advice.