When I was in this position you are in now I got great advise from both Woman's aid, and my local woman's aid shelter. You should be able to find this information on their website.
Firstly, if you have a friend you can confide in, or a family member get a bag ready with the following and leave it there with them for the day you leave.
Secondly, did you know you can now go into any Boots and ask for assistance?
They will take you aside and give you advise on the next steps.
if you can gather the below prior to leaving all you then have to do is scoop your lil one up and go.
Passports
important paperwork
Clothes and toiletries
mobile charger and any charger you may need.
(if you need to change your mobile number then you can call your mobile provider and ask them to change your number, if you have to, due to domestic abuse.
If you dont want to change your number but dont want him to contact you to intimidate you, then get another sim card and only give out your new number to those you trust. Then use an old mobile for your current number. Its just so that you get time away from whatever he may throw at you.
Make sure that whatever internet browser you use, to go icognito.
Do have your mobile phone checked over for any apps where he might be able to locate you, that is if you leave to a womans aid refuge. They will have to relocate you if he finds you.
What your partner will do once you leave may be frightening and his behavior may become erratic from being threatening to very loving, begging you to come home, and in the same minute, if you don't comply, to tell you what is going to happen. He will threaten to take your child, they always do this. So you need to keep calm and never go back once you go because this is what I found out once I left, 3 times in total, two different woman's aid refuge each time, was that its easy to leave, but so hard to stay away. Why? well for me I knew my ex tactics, but I did not know how unpredictable he would become once I left and didn't do as I was told anymore, and so he would revert to all sort of characters in order to charm me, frighten me and threaten me.
I went back home again twice, the third time I left was the final time.
Once you leave, do not negotiate with him on your life. You dont own him your life, or the life he has left you living which is no life at all.
Call womans aid, and if you dont get through the first time, try again, they have the option to call you back, and give them a safe time to call you back, not when he is home. If he is likely to know you are about to leave he is likely to charm you, or become the person you once fell in love with, please understand this is a form of manipulation as an abuser will feel anyone leaving them is denting his ego on the outside, so he will try and avoid you going by being charming, or threatening.
The police, depending on the information you give them, will likely come to your home, this is just to see if you are ok, and also to log this. Please speak with your GP as well as this will then be logged with them as well. Your ex may get arrested, he will be told not to contact you, but womans aid will also be able to say what is likely to happen if you report your ex to the police.