Put in a formal complaint to the Chief Exec about the delay. Complaint policy will be on council website
I would also ring the local govt ombudsman - usually you have to go through the council complaint process first - but explain your child is already effectively out of school, not receiving a FT education since May, there are 2 weeks left to view any other schools LA may suggest and LA has sat on case since 31 May. Tell them you can't appeal to SENDIST (I am assuming you have a statement?) until the LA make a final decision which gives you an appeal right - which they have not done since 31 May. Ask if LGO will take the complaint early.
I would then write to your SEN officer -say given the timescale you have now had to make a formal complaint and have referred the matter to LGO. Say that as the LA has delayed in investigating alternative options and your DS currently has no school place for sept, and there is now no time to view any potential schools, that you require them to put in writing how they intend to meet your child's needs out of school in Sept. eg via home tuition
Agree also go to MP and copy all letters to MP
If having your DS at home is a problem e.g. as you work etc? You may need to have a social care assessment for disabled child / carers assessment so you can buy in childcare. Keep details of any costs you build up e.g. loss of pay etc so you can go to Ombudsman later and ask for these to be repaid.
There was some talk on here in the past about cases where LA delayed in amending the statement after review and whether their non response could be taken as a refusal to amend and you could persuade SENDIST to take the case even though you did not yet have the written notice. I don't know what the outcome was whether SENDIST would intervene or you would have to use LGO to get the decision and then appeal. You could ring SENDIST and ask if its essential you have the written notice or if non action can be taken as refusal to amend.
328A Education Act 199 (added in 2010 under Chiildren and Families Act) gave a right of appeal against determination of local authority in England not to amend statement following review
(1)This section applies where a local authority in England?
(a)conduct a review of a statement in accordance with section 328(5)(b), and
(b)determine not to amend the statement.
(2)The authority shall give written notice of the determination and of their reasons for making it to the parent of the child concerned.
(3)The parent may appeal to the Tribunal.
(4)Subsections (1A), (3), (4) and (5) of section 326 apply to an appeal under this section as they apply to an appeal under that section, but with the omission of subsection (3)(c).
(5)A notice under subsection (2) must inform the parent of the right of appeal and of the period within which the right may be exercised.
(6)A notice under subsection (2) must be given to the parent within the period of seven days beginning with the day on which the determination is made.?
I suspect if pushed the LA will name the current school - make you appeal - and buy themselves time as an appeal will not be heard for several months. Has the school actually refused in writing to have him back in Sept?
If your child cannot attend the current school in Sept either as no school place or because anxiety then LA have a duty to provide education out of school e.g. a home tutor.
Look at LGO report on their website 'out of school out of mind' and info on IPSEA about rights when a child is not accessing FT education and what LA should be doing.
Are you eligible for legal aid?
Once they know you will expect home tuition there will be an incentive to move things on.
Where do you want your DS to go? Do you have a school in mind? Do they have places in Sept? Be worth finding out / doing a visit of what you think is suitable.