Ring Council and ask for emergency accommodation, they have a duty to put a roof over the kids head, so will find you something. It might be a bedsit or b&b to begin with, but you'll go on the list to get something long term.
Start a universal credit application. You don't need to wait until you move out. You are no longer a couple, so the claim can start immediately. You won't get any actual payments for 6 weeks, but can get an advance to see you through.
Call citizens advice, ask for them to signpost you to food banks and depending what type of accommodation you get, possibly community furniture scheme. Plue take any other help they offer or recommend.
Once the kids go back, ring the school and explain. They'll be better able to keep an eye on the kids, and may be able to offer some discretionary help (could be advance on school dinner payments, sourcing second hand uniform if they need anything or funding any trips until your back on your feet)
Sign up for local pass it on sites. Look out for any furniture, bedding or household bits you need.
Do anything you can to make that job offer work, you'll need it now more then ever. Look for childminders or nursery's that pick up afterschool kids. If you have a class WhatsApp or mum friends, ask what they use.
Good luck!