@Nicola6410
The first thing to understand is that regardless of why he's gotten a wild hair up his arse, you can't stop him from leaving and you won't be able to make him step up with the DC. So you need to be thinking only of yourself and your DC.
The deposit is solely in your name? Good! Consider it your 'severance' pay and keep it. If it's in a joint account, move your share or half (whichever is greater) to an account solely in your name. Call the estate agent and cancel the house purchase. If there are any refundable deposits or securities paid, be sure they come back directly to you.
And whilst we're on the subject of money, if you have joint finances, separate them immediately. If not, just to be on the safe side change all your passwords. In fact, change passwords to any/all things in your name like utilities, TV packages, etc. You need to realize that as of this moment you are a single parent. Protect yourself and keep protecting yourself, regardless of the outcome.
If you can afford where you're living, even for a few months, stay put (for now) and tell him to leave. Say that since he is the one who wants out, he should be the one who leaves so the children are as least disrupted as possible. Use this time to catch your breath and make more permanent plans for your future. Don't rush in to anything. Other than rushing to file for CMS. If you can't afford it on your own, stay put anyway, but begin to live as a single person. I don't mean dating, I mean making your own decisions, separating finances as above, and STOP doing any 'domestic services' for him. No cooking meals other than for you and DC, no doing his laundry, shopping, life admin, cleaning up after. And either move into another room if you can or tell him to sleep on the sofa. In other words, no sex and no sharing a bed. He is no longer your partner. He is your 'roommate'.
Please, please call your mum and your sister and let them know what's going on. At this point you really don't know their situation or their ability to be of practical help to you. Only when you find out how much of a help they will really be can you make your plans. It may be better for you and DC to move, not to London, but to somewhere cheaper but farther away.
You'll get through this, you will. Just stand tall, steel your emotions, and think about yourself, first and foremost. And do not do the 'pick me dance'. If he is 'done' with you, you must be done with him. Keep your pride and your dignity. You will be glad you did.