@Secondtimemum24 - I expect you are feeling a little overwhelmed right now, both because of the situation you are finding yourself in, and also because you are probably afraid of him trying to get your baby for overnights etc.
When situations are overwhelming and scary, it can be useful to break them into different parts and tackle each one separately and methodically.
First and foremost get him out of your house, and change the locks. Once that's done, you'll be better able to breathe and focus.
Next, write down everything that has been happening, especially a detailed record of his lack of parental contributions, both practical and financial. (Your OP is a good starting point.
Also list and evaluate the advice you've received in this thread.
Tomorrow call Women's Aid for advice on the best way to proceed.
Next contact a couple of experienced family solicitors with a view to ensuring that he gets no overnights until the baby is at least 18 months old, and until he has suitable (self-contained) accommodation. Make a list of your questions and concerns before you call.
Also initiate a claim for maintenance with the CMS.
Depending on your financial situation, you may also want to look into getting universal credit.