Adult social services (ASS) for an 'urgent needs assessment', and if you are going to be visiting him when he is in hospital, then learn the words "unsafe discharge" and bang on from the beginning about how worried you are that this will be another one. If the flat is as grim as you perceive it, then every time he is sent back to it from hospital without them having seen it, is an "unsafe discharge" once they're aware. They should then send him to a hospital step down unit while social services assessments and potential provision is put in place.
These units where created to stop bed blocking while providing non emergency level medical care and rehab. They're intended to ensure cycles of ongoing medical issues ending in repeat hospitalization caused or exacerbated by a lack of needed disability/age related help, housing issues, mental deterioration, alcoholism, self medication etc, were broken.
Your father is an absolute candidate that they were designed to try and sort out holistically following acute medical intervention for one part of his issues only.
The hospital 'offering him a daily carer' will have been either a hospital OT or SW filling out a referral form to adult social services, saying they have assessed him as needing this help. He is automatically entitled to six weeks of carers as 're-enablement' (prior to financial assessment for it to be ongoing) if he was in for long enough.
If you don't want to step back, then I'd suggest working out which dept was assessing him prior to discharge, and getting in contact with them asap at the same time as contacting ASS. IME they can still issue this letter post discharge.
When talking to adult social services you need to be talking about how it will make the situation so much worse and how many more services will be needed if he ends up an amputee through all this. (Sorry if it's dispassionate, but it is the bottom line of it all for them.)
Additionally email/write to the GP. They can't discuss anything with you, but can try and sort out things like medication feet etc and provide valuable back up with adult SS once made aware.
As with all things nowadays, services are stretched and not everyone will or can do their jobs especially if he's handily providing them with refusal to engage or saying you will be helping him. Some will also write you up as able and prepared to do things you aren't unless you constantly say this will not be happening. (A good example of this is ' the patients adult DC will let in the carer four times daily, while knowing the DC to be at work. It makes it appear care is being provided which can't actually happen without the interim step of a key safe being fitted, but allows that person to close the case.)
You have to chase and be a nuisance (the crying baby gets the milk) or step back totally, as unfortunately half way measures will just prolong the current situation until something dramatic enough happens to bring it to a head again. Either is reasonable in your circumstances.