Get out the house ASAP and quietly.
If you don't work weekends, tomorrow is ideal, and if you do, you tell them you have an emergency you need to deal with. This gives you time to work with while he is still sleeping until the afternoon.
You don't need much. Just as much as you can put in a bag you usually take out - important documents (passport, birth certificates, tenancy agreement) and a change of underwear and any medication if you take it.
Don't give any indication beforehand or panic. Let on you are taking you and your LO on a walk, or to the shop.
Once you have left the house, go to your mums. If you can't afford this, contact your mum or someone who can help you get there. Do not make plans on your phone before this, as if he looks at your phone etc he will see this.
Once you are safe in your mums, this is when you contact police. You will have support there for you, and your LO. You tell them that your partner is refusing to leave your house, despite not being on the tenancy and has threatened to kill you if you leave him. They will be able to see his previous from just having his name and they will take action THAT same day.
You need to arrange for the locks on your house to be changed, and if you cant afford this, you can ask mum for a loan or last resort you can reach out to LL and explain the situation and tell them to put the bill on your next payment instead if they can do this now.
Even with the locks changed, I would stay away from the house for a couple of weeks at least, for safety reasons. I am not sure if he will be bailed, but usually even at that, bail conditions will have that he cannot contact you or be near you, or the address or he will be arrested.
Once you return home, you lock all doors and windows religiously. If he is stupid enough to come round to the door, you tell him through the door or window to leave, and then you call 999 immediately.
I wouldn't be putting up with a lazy, abusive slob like him that contributes absolutely nothing to your life but pain and misery.