The amount of ignorance on this thread is astonishing.
Anxiety which prevents a child from attending school absolutely is SEN, as pointed out by PPs it is specifically referred to in the SENCOP. This anxiety often derives from undiagnosed SEN, schools have cut funding, they simply don't have the resources to diagnose bright children with things like dyslexia or masking children with ASD.
I would have sworn blind that my school refuser had no SEN it wasn't until the wheels fell off when trying to force him into school when anxious and he tried to kill himself that we requested and ECHNA and this uncovered complex.needs, asd, spd, dyslexia, clinical anxiety and depression and trauma from trying to force him into an incorrect environment.
His alternative provision was full time. He did his GCSEs at home, invigilated, and fully funded by the LA who acknowledged that there was no school that could meet his needs and he has now reintegrated to a mainstream selective 6th form for A Levels with a view to going to University. He has been able to do that because we removed him from the inappropriate environment and had his theraputic needs addressed, also funded by the LA.
Now the OPs son may well cope with a part time timetable but an assumption, because nothing is diagnosed that there is nothing other than a bit of worry that he needs to be forced through is incorrect and potentially harmful.