don't think he would be classed as intentionally homeless if he's received a valid notice to terminate the tenancy
He would be, in many places. You often can't leave until the bailiffs evict you, if you want help from the council.
He has a lifetimes' worth of possessions, a washing machine, a fridge, two bicycles, art work, chairs, double bed, tables and other furniture etc. his current flat is unfurnished, he has furnished it. Does he have to lose all his possessions along with his dignity?
Unfortunately that is often the case when you're homeless, unless you can afford to pay for a storage unit or a friend can store your possessions for you. I advise anyone who plans to use the council's homelessness procedure, and who doesn't have storage options, to sell anything they can. Because if you're going to lose it anyway upon eviction, you may as well get some money for it.
I'm fully aware that sharing may be his only option, I'm trying to help him avoid it. If it happens it will be a fast route to depression and giving up
At which point he'd be eligible for rehousing on MH grounds. Basically, you often have to be almost dead before you get any real help, sadly.
might be worth getting an appointment with a social worker at the council,
They're allocated based on need. You can't get access to a social worker just because you want one.
What you can more easily access is a Tenancy Support Worker. Either via the council or a charity. They provide help in accessing and maintaining tenancies, helping to overcome any obstacles to that. Investigate the charities in your area OP and ask the council too. Someone in your friend's position is likely to be eligible although sadly there may be a waiting list. Keep them informed as a change in circumstances could move him up the waitlist.
Over 55s via the housing association via the council's homelessness procedure is the best long term option, but in the short term probably will mean some form of shared temporary accommodation eg a hotel room. In my area at least, the one bed flats for temporary accommodation are reserved for families (there is no larger temporary accommodation). Sometimes they're given to the mentally ill, which is why persuing diagnosis (where applicable) is important.
OP your friend can register with the council even if he doesn't go through the homeless process. He can still bid on property whilst securely houses in a new private rental if that's the route he chooses. He'll just be a lower priority and will likely wait years. Although not as long as for a regular property because obviously the over 55s ones become available more often as mother nature takes her usual course. He can update his information with them if he ever faces eviction again. It's worth doing because the time you've been on the waitlist is taken into account when allocating properties, if all other circumstances are equal.
PIP doesn't depend on diagnosis but your symptoms are more likely to be believed if you have a diagnosis to link it to. Without a diagnosis you need more medical backup than with.
People are disabled whether they claim PIP or not, but the successful claiming of it is often the marker used when officially recognising someone's disability for the purpose of allocating resources. There's various help and support to those claiming PIP that isn't available to those not claiming it. It's shite but it's how it is.
As others have mentioned, he should also check with the utilities companies about their discount schemes for people in poverty, which he may qualify for.