Practice may vary between areas, but here the police will return with the woman to collect belongings. Social care would have referred her for a refuge place, where she would be able to stay to start with.
They would also refer her to a service that will support her to go to the council, who will have a statutory duty to house her and the children. Once they have temporary accommodation (but not B&B!) available, she would then be supported to move.
She would also be helped to claim benefits, to change addresses on all a/c's etc, to access legal advice, liaise with schools (sometimes, children have to change schools because of risk of abduction or risk to the mother at pick up/drop off), apply for maintenance, access MH services if necessary etc.
If they own their house, and it's not in joint names, she will need to apply to the Land Registry to get a matrimonial rights notice registered (it's really easy to do and is either free or very cheap, a solicitor will charge for doing it).
She'll need an address for bank statements, new cards etc to be sent to and set up mail forwarding. Sometimes, it's safest to get a PO Box address, it has been known for an ex to find out the forwarding address if they know a dodgy postie!
She will also need a lot of support and reassurance from her friends and family though. It will be very traumatic for her and she will feel very vulnerable. She may become very depressed and doubt that she has done the right thing. She may start showing signs of PTSD (as might the children, if they have seen their father behave in a way that has frightened them). Hopefully, the refuge will be able to link her in with an agency that will help.
Maybe you will be able to provide some of that support, OP. If so, take care of yourself, too. Helping women resettle after fleeing DA used to be part of my job and some of us found it incredibly draining. My manager agreed that we would only ever have one DA case on our caseload at a time (luckily, there were 2 others on the team who were excellent at this sort of work and seemed better able to maintain some distance, I think it was hard for me because I have been in 2 abusive relationships myself).