OP. you need to start with the basics.
Are you working or will you go back to work in the new year? Do you have any savings.
Work - I became a single mum when I returned to work. I found the only way I coped was to find a small flat and a child minder very close to my work. That meant I could drop baby off on the way to the office and collect on the way home. It made life easier and I was never far away if he needed me.
Housing - If you cannot afford to rent a flat of your own, talk to the local housing department. Tell them you are about to become homeless, that your partner is going to kick you out. What can they offer? The ideal would be a one bed flat, cheaper to rent/heat/quicker to clean. Baby doesn't need their own room for years. They may only be able to offer you a room in a hostel which isn't easy.
Money - Life will be much easier if you have a deposit for a flat, or at least a bit of money saved to pay for the basics if the flat is unfurnished. So save as much as you can while you are still with your partner. I knew my split was coming so I managed to save a deposit.
Benefits - check online what you will qualify for. And check the CMS calculator for what your baby's dad will contribute. Work out what your likely income will be.
Support network - Re-establish relationships with family members if you can. Even a little support network is better than none.
Once you have a plan & a budget, you will start to feel more in control. It took me about 9 months to get organised. Work to a schedule that suits you. Good luck.