Is the CIN plan still in place?
In any event, if your dc was in the house at the time your partner made the threat SS will be notified as a matter of course.
Are you married? If not, are you living in a property that is solely in his name? If it transpires that you have no right to remain in your current home, I would strongly urge you to ask Women's Aid to provide a refuge placement for you and your dc where you will receive the support you need to break free of this untenable relationship, to sort out your debt issues, and to apply for social housing.
As it's not the first time he's come to the attention of the police for dv, I would hope that he's given conditional police bail which prohibits him from making contact or coming near your. He may be bailed to live with his dm, if she'll have him, pending further enquiries or he may accept a caution in which case you'll need a non-molestation order to keep him away from you/your address.
As the Women's Aid national helpline tends to be oversubscribed on Monday mornings, find your nearest branch here and make contact asap www.womensaid.org.uk/domestic-abuse-directory/
However, I would hope that the police will allocate a dv worker to your case and that they will be in contact with you later today.
If you don't hear from the police by, say, mid-morning I suggest you give them a call to find out whether your, hopefully now ex. partner has been released and on what basis.
Failing to press charges on the previous occasion was not in your best interests and it's to be hoped you won't make that mistake again as your dc deserves considerably more than being raised in a toxic environment.
Good luck - I'll look out for your update later today.