Single parent in London - Final Year

Hi everyone, I am in a very stressful situation and hoping for some advice. Long story short, I am in a relationship that seems to be coming to an end with a child who is now 7, my current partner is not her father.

I live in London in my partner's house with no other family in the UK. My daughter has no contact with her father, so I am completely on my own. My mother was my only one family and I lost her 5 months ago. I am in my final year doing a very hard course, but I had to interrupt as a result of the ongoing stress in my current relationship and losing mom.

I have number of problems I am facing, and the one that worries me the most is housing arrangements for me and my daughter. I know London is having a huge crisis for housing at the moment with thousands of people waiting for housing, so that does not fill me up with confidence.
I will not be able to work full time because I am also full time in uni and have to care for my daughter, so I don't think a private landlord will let me rent a house. Next thing is money and financial worries whether I will be able to manage.
My head is a mess and I feel completely alone and not seeing a way out of this. I will appreciate any advice from people who know or are in a similar situation to mine.

Hello, have you gone to the council??

I have, they basically told me that I need to become homeless and contact them when that happens. The thought of that terrifies me I won't deny