Hi OP,
I understand that the legal position is that in the event of a formal exclusion, on the relevant day school must contact you, but if you cannot get there, they have to hang onto your child until normal collection time.
Thereafter you cannot send your child in until the exclusion has expired.
My 10 year old had a 5 day exclusion in the summer term. I went for him as soon as I heard but it took 40 minutes. When I got there he was semi-foetal, sobbing in the head's office, absolutely distraught. I cannot conceive of not getting to him asap. Exclusion is one example of something for which you can get statutory parental leave from work (unpaid).
I put in for stat ass myself in July. My LEA agreed to assess and mid-October they agreed to issue a statement, though it will take time for that to come through. There was an extra 4 weeks allowed for reports to be submitted because of the summer holidays. So whilst it does take time, it will not take less time if no request to assess is submitted and the initial request to assess is pretty simple and can be downloaded as a template from Parent Partnerships websites.
As for a part-time timetable or unofficial exclusions, they are as dodgy as everyone here is saying, but my experience is that very occasionally, whilst you wait for support to come through, they may possibly have a place if they can be handled without too much stress for you as a family.