My daughter home schools all her children. They all have varying degrees of autism, and cannot cope in mainstream education, yet none of them are considered to have severe enough problems to be eligible for special school education.
She has a yearly visit from the LEA to assess her teaching, and the children's knowledge. They go through all the work books and all her curriculum material. They asked where she sourced her teaching material, and how much it cost, if it wasn't a free resource.
At the last visit the lady from the LEA wrote down some of the websites my daughter had found for teaching geography and maths, so that she could pass them on to other parents struggling to find good teaching material.
In all the lady stayed for over four hours. Her inspection was very thorough.. My daughter was given a glowing report and told to keep up the good work.
My grandchildren do all sorts of other activities outside the home too. Kayaking, art group, folk group, and regular home school meet ups. The children have lots of friends, and none of them want to go back to school.
If the LEA found that the children's education was lacking, they can insist upon them going to school.