Then you must complete thes elf assessment as self employed until Sept 2013 and then as employment from Sept 2013 -
Once you have the tax returns into HMRC then write to HMRC making reference to the tax returns challenging the fact that the charity took you on in a self emplyed capacity which you feel is wrong (and this is further supported by the fact you have since Sept 2013 been taken on under PAYE as an employee
Ask HMRC to challenge the charity on your behalf, and explain that you would take this up initially yourself but due to your ill health and their subsequent treatment of you - do not feel able to manage this directly -
Also in your letter empahise again the reason for the dely in completing the tax returns and advsie that you have paid all the fines - which you on hindsight do not feel shoud have arisen, as you should not have needed to be in self assessment if you should in fact have been an employee.
Take a screen print of the ESI tool view of your employment status and also enclose this - and advsie HMRC you are willing to assist them with this matter in any way you can.
I also would advsie you that you consult with an employment lawyer (initally consult ACAS who offer free advise) - link here for ACAS http://www.acas.org.uk/index.aspx?articleid=1410
as you also should consider what might be owed with holiday pay, sick pay etc as I do believe that with the type of work you were engaged to do for this charity there is no doubt you were and should have been an employee from the start as you have o change of duties and were working for the charity and not yourself.
Let me know if I can be of any further assistance