This is upsetting for you, but not as bad as you fear.
7 is still young, and enough time to catch up with formal things - I'm sure that they have learned plenty, but probably can't respond in a formal manner. Neither would I worry too much about reading - they will pick it up quickly once helped.
Please don't let the children pick up on your worry (or your anger with their mother) - they will be confused and upset enough without having to worry about your reaction.
Whilst your DS needs to take action to put this right, social services will understand that not all children go to school or are brought up in the same way.
I am assuming you are in the UK?
Un less you have very specific concerns unrelated to their education, I would contact your local school initially. They will have a strong relationship with Children's Services and will involve them if necessary. Most schools are used to taking in children who have been educated differently or in different systems.
Unless there is any suggestion of abuse, it is most likely that SS would want the children to stay with their father and you. They would not wish to remove the children from a loving family environment. They may need to do an assessment to formalise that. Your son should not worry that simply attempting to educate the children differently is not in itself abusive.
You don't say what the mother thinks of him taking the children and moving in with you. However, even if she disagrees, your position will be strengthened by going into school.
Can I also suggest that you no longer 'test' the children? They will want to please you and it may worry them if they can't do what you expect. Given time, I am sure this will get sorted out. I have known children who have had no formal education until this age, and all other things being equal I'm sure they will be fine.
Good luck - this is a lot to be dealing with.