As you've discovered, local authorities and other agencies that can loosely be regarded as 'professional' or 'specialist' in the field of child care and welfare can't be trusted to get it right or keep their promises are frequently persuaded by politicial budgetary reasons to cut corners and thus fail to source placements which will provide the best possible outcome for children such as your ds.
When I attempted to give a potted history prior to your initial appointment with Bindmans, I outlined your complaint in law as being in three parts, each distinct but interlinked by virtue of the fact that they have bearing on your ds's past, present, and future care needs.
As I've said, IMO your/your ds's case against SLaM is irrefutable but, given what you've said, there is a much bigger issue than his traumatic stay at, and removal from, the Bethlem and that is why it has been necessary for him to be an inpatient at any mental hospital.
You've said that your ds has been in 48 placements and 6 mental hospiitals and this begs the question of to what extent your local authority's and/or other agencies historic failure to make appropriate provision to meet his needs has contributed to the mental ill-health he has suffered over the past 18 months.
In addition, although his current alleged mental ill-health may require inpatient care and treatment, it is my belief that consideration should be given at this moment in time as to what provision will be made for him on discharge as the outlook will indeed be bleak if he remains within the confines of a mental hospital until he comes of age and beyond.
I would suggest that, if you haven't done so already, you raise the above with your solicitor as it seems to me that the Bethlem is, in effect, the least of the complaints in law for which you should seek redress.
With regard to your ds's useless current legal representation, I would advise you to be guided by Bindmans and I would also suggest that you seek advice as to whether, by virtue of being under section, your ds is considered competent in law to instruct a solicitor or handle any of his own affairs.
It goes without saying that I have every confidence that you will act in your ds's best interests and, to this end, it may be expedient for you as his nearest relative to obtain authorisation from your ds to act for him in respect of appointing a new -shit hot-- lawyer to represent him unless, of course, he is subject to a care or other court order.