OP, this time 3 years ago, my husband of 13 years did exactly the same. I am sorry to say that there was an OW despite denials and him just wanting to "be on his own", my youngest was 2.5 and undergoing diagnosis for autism at the time. I am sorry to say that his promises of still paying the bills yada yada yada stopped very quickly.
My advice to you is get into a solicitor quickly. However shit you feel, photocopy everything, ensure you have access to bank accounts, credit cards, have copies of all certificates, passports. Inform everybody and change passwords if necessary. Tell your mortgage provider. Apply for benefits if necessary, sort out council tax, get all utilities, Sky/whatever in your name, car insurance, mobiles etc because the shock of all that being cut off floored me.
I am being hugely practical here but I KNOW, I totally know the heartrending, soul destroying pain that you are dealing with now. I can tell you that you will get through it, I can tell you that your kids will survive, I can tell you that you will emerge stronger and amaze yourself with what you are capable of.
Keep posting, talk often, take every last bit of help you are offered. Eat as much as you are able, even if it's just soup or a protein shake, expect to lose weight. Keep hydrated, try try try and sleep. Tell the children's school asap. Get to know the school family liaison/welfare person. Tell everybody, don't be embarrassed, you need the support. I know none of this is easy. I still bear the scars but my God is life better....it really is.
I send you huge hugs, a hand hold if you need it and a promise that you will work your way through this, that there is life on the other side and that he will fucking well regret being such a twat in years to come. 