If they keep refusing carers...

I’m pretty sure it doesn’t work like that - my understanding is that if there is a need then that need has to be met. Hopefully someone who knows the Care Act will come along and answer properly.

However, some councils are moving to an assessment system that is less focussed on ‘needs = paid carers coming in’ and more focussed on ‘ok, what can you do, what social resources do you have, what do you need, how can we get that done in other ways’ like vdb’s suggestions. The danger for you in that is that you might get emotionally blackmailed by DF into doing more than you can manage.

Does he have a particular problem with the carers or is it just that he doesn’t like breezy strangers wandering in and out of his home and doesn’t like the loss of independence?

If he has capacity then yes he can decline it but if his care contract is closed and in the future his needs change then SS would do a new referral and care act assessment. It might be worth getting a health and welfare power of attorney put in place so that in future if his mental capacity goes down you would have the power to make sure he is having care that he might need but not necessarily want it you follow me?

If your father has capacity to decide to refuse - and the legal assumption is that he does, then he retains the right to make what others might consider an unwise choice.

It might be worth talking to the social worker and your father to look at alternatives to enable hims to retain his independence. Hot meals delivered, something like Wiltshire Farm microwave meals and a fixed setting on the microwave or sandwiches even. Is there a neighbour who might cook an e tea portion and drop it round each evening for small recompense?

Medicine can be put into a dosimeter. Some have timers and alarms to remind people to take them.

They have a statutory duty to assess and signpost towards appropriate care. Depending on income, they may or may not fund it. They can’t refuse because he’s refused in the past.

My sister and I arranged for carers to go into help our mother, she refuses all help, but we have continued with the carer going in, she just goes in, asks my mother how she is, if she needs anything. Mother always says she is fine and needs nothing; carer signs her book and leaves.
We leave the contract in place, because we know there will come a day when the carer is needed.

If he has capacity, then he’s entitled to refuse anything he likes, including life saving treatment.
Do you think he’s reached the stage of lacking capacity, eg due to dementia? If so, you could approach his GP and SS on that basis. If not, then he just has to suffer the consequences of his own stubbornness - all you can try is gentle persuasion.

slightly missing the point here with my reply but would be be happier with a meals on wheels type service where they deliver a ready to eat meal rather than a career come in? If he has a lifeline pendant, they will often have medication prompts as part of that service where they will phone and remind you. Or a medication dispenser that will alarm at the time of a medication and keep alarming until you take the pills.
Re SS, they will be used to this scenario and I would hope, will continue to try and help persuade him.