Shame him ! Write to his employer, explain that you and your 3 children have been deserted and ask if money can be diverted from his monthly salary to help you pay the mokrgage and meet your bills.
They undoubtedly won't do this, but if they call him in and let him know that they're aware of his behaviour, he might pull his socks up and send you some money, if only because he's worried his employer might think he's not a very reliable kind of person to be employing.
Of course you must speak to your mortgage lender first and see if they will give you some financial leeway or allow the mortgage term to be extended. And what are your relations like with your partner's parents? Surely they would be concerned about the well-being of their grandchildren? Would they be able to put pressure on their son to meet his financial obligations? It's worth a try.
And have you tried contacting the Child Support Agency? I know they don't have a good reputation, but you shouldn't leave any stone unturned if you've had no financial support from him for 9 months.