Okay.
This is going to be tough, but you CAN get free of him.
First, squirrel away some cash savings if you can, and stock up on food shopping, make sure toddler has clothes in the next size up, make sure your phone has lots of credit.
Then, tell him the relationship is over and ask him to move out.
He won't move out, but that is beside the point at this stage. (If he does go, great, change the locks and don't let him back).
Then, move into your toddlers room to sleep, or onto the sofa, if there is no spare bedroom.
Stop doing anything for him - no cooking, laundry, shopping. Shop only for yourself and toddler.
If you think there is any chance of him getting violent, or if he start to show signs of losing his temper, phone the police immediately. If you already know he is violent, phone them in advance as a first step to give them a head's up.
He will try to engage you in talking about it all, reconciliation, promising you the earth, promising it will all change - don't believe a word of it. He won't change. Stay strong and don't talk to him until he has moved out.
Next:
If you have joint bank accounts, contact the bank to get your name taken off, so they become just his accounts - you might want to take out half the money first. (If the accounts are overdrawn, you may have to pay money IN to get your name taken off, so ignore this step for now).
Get yourself a current bank account in your name if you don't already have one.
Then - tell the HA you have asked him to move out but he is refusing, and ask for their advice.
Then - put in a claim for Universal Credit as a single parent, and housing benefit for the rent and council tax (assuming you don't have over £16k saving in your name).
The UC may take a while to come through, so be prepared - hopefully you got some cash put aside at the start and stocked up. Can you use supermarket points for shopping? Can your family help out with shopping?
Then, put in a claim for child maintenance from him with the CMS - you can do this even if he is refusing to move out.
When you get some CM or UC coming in your name, then contact the utility companies, TV licence, Water, etc. and get it all put in your name, with Direct Debits coming from your bank account. Cancel anything you can do without, such as TV subscriptions. Change the Wi-Fi password.
Then, look at a long term plan - which will be you working while DC is in nursery then school. Look at childcare options ready for when you get a job.
He gets NO say in this.
Eventually, he will see the writing on the wall and move out. If he still doesn't, ask the HA and police for advice.
(Where he goes is really not your problem, so don't let it be an excuse that he has nowhere to go).
Best of luck.