I'm sorry things have been so rough for your son at school. The last survey I saw from the home ed charity Education Otherwise identified unmet special needs as the number one reason for kids to be removed from school for home education, so you certainly aren't alone in that. 🙁
Home education is far more efficient than school, and can be done whenever you want, so you'd have no difficulty giving your child a good education during the hours you aren't working. So the challenge for you, as for many working parents who home educate, is all about childcare.
Might a childminder, babysitter, or nanny share be an option? If you're exploring this with them, reassure them that you don't need them to provide education, only childcare. Some providers imagine that it might be illegal for them to look after a child during the usual "school hours" without providing education, but that isn't the case. (Of course, you know that your child WILL be learning when he's being minded, through discussion and playing and so on. But that doesn't have to be formalised.) I used to use childminders who were themselves home educating their own kids, so they took mine along to home ed activities and it worked really well for all of us.
If you're on Universal Credit, you can claim back part of the cost if you use registered childcare, just the same as if you were using a setting after school. It works exactly the same.
You might be lucky enough to find some sort of drop-off home ed forest school or similar in your area, but they aren't very common and might not fit in with your needs and schedule. Most home ed activities are run on a voluntary basis by other parents and would require you to stay.