I've raised £20000 to help save our home

We live in my ex partner's house. The mortgage is in his name only. We had an on-and-off relationship for a few years, but decided we work better if we're not together. We have 2 children. Before he met me, he had a brief encounter with a woman who got pregnant. He vehemently denied the child is his, despite a positive DNA test result. The CSA got involved, they calculated child support payments and kept coming after him because he refused to pay. The debt kept piling up and in the end they took him to court to force him to sell his house. In which me and my children live! The court sided with the CSA, not caring there are minors living in this house, not caring we practically have nowhere to go! I went to my local council, but was told if I submitted an application, I'd be refused because I'm not a British citizen. My son has autism, he's not yet speaking as well as he should at his age (he's 4), I just managed to potty train him, and he has frequent meltdowns. Having to move out of our home would completely upset him... I'm at my wits end, I don't have any idea what to do, how to tell my children we will end up on the street! I haven't got much time left to pay off his debt, otherwise we will end up rough sleeping!