Hello BB I've read your Original thread. I'm a retired social worker (Children's Services) and have 30 years experience all told. Firstly the GP has absolutely no rights whatsoever to dictate on your living arrangements - she can suggest or advise, but NOT tell you what you have to do - I've never heard of such a thing. Shocking.
As far as child protection is concerned, a social worker has no authority to remove a child from your care, contrary to popular belief. They have to apply to a court and have to provide evidence to the court that the child is suffering (or likely to suffer) significant harm and believe me they need hard and fast evidence. Also request to remove a child is a very last resort and so I really think you should stop worrying about that. How old is your son? It sounds like he has special needs? You mention he used to have a social worker from the disability team - but presumably this has ceased. Is this something you might find useful, though not saying that you'd get one, as Social Care (like all public services) are struggling with severely depleted budgets and so can't provide anything very much, other than comply with their statutory responsibilities. Thanks to the coalition for demanding massive savings in budgets.
What is your MH diagnosis? Is it depression/anxiety? Are you on meds, though I think you mentioned counselling too. There are hundreds of people with MH issues who are caring for children, and a diagnosis of depression/anxiety is not going to be considered by the LA as a reason why you can't care for your son. If a parent is trying to cope alone and suffering from psychosis (as in being out of touch with reality) then IP care is usually needed and the child might then have to go into temporary foster care until the mother has recovered.
SO I would say NO - this is not going to "turn CP" if you ask your son's father to move back home but would welcome him calling in to make sure everything is ok, or even staying for 2 or 3 nights (whatever you think would be best) I suspect it might suit your ex to be living with you rather than at his own place.
You have a right to Access to Medical Records, so you could google to find out the process with the NHS. I would be tempted to make a complaint about the GP who gave you mis-information on this important issue.