God I really feel for you. Try to keep eating, small things but regularly if you can.
Also, do have joint bank accounts? Joint savings? You need to check the accounts and make sure any money is still there and then transfer half of anything, if you can, into a single account in your name only. (cynical emoticon)
If you don't have an account in your sole name, set one up. For tax credits and Child Benefit to go into.
You will be ok as tax credits will help keep you going. Call council and tell them you are now single and claim 25% discount.
As for his things, I agree with the others: put stuff into bin bags. You don't have to gut the entire house of the git's possessions....we're talking toothbrushes, clothes, shoes, ties, deodorants, shampoos, that sort of thing.
Is the house in joint names? owned or rented?
Just keep breathing. You WILL come through this, I promise. It seems nightmarish at the moment, but the truth will come out at some point and you will see the man for what he is: a spineless shit.
Keep posting. 