Is there a seat in his wet-room? If not, you could get one. After he's washed his butt, he can sit on it whilst he washes the rest of him, feels safer, less risk of falling, he sounds the proud kind that would never admit he's struggling.
Does he know where his local launderette is? He can pay for a service wash if he doesn't want to wash his own clothes. Or could you all club together and buy him a washer/dryer for Christmas? Use s red pen to mark the basic wash/dry cycle. Show him how to turn it on, put powder into the drum (because he's never going to clean out the powder drawer) and press start. Ensure he knows to take the clothes out as soon as they've finished to minimise creasing and going mouldy from being left damp from the steam that's still in the machine. Part of the problem could be he just doesn't want to admit how much he struggles with technology, so blames it on "women's work" instead. Although he does seem to have a bit of an attitude problem there towards women, a generational thing perhaps, a dislike of change and a refusal to move with the times. A large part of why he smells will be his filthy clothes. Clothes are so cheap now, if he doesn't want to wash them he could buy a new set every week to put on after his shower and would smell infinitely better, although it's a wasteful way to live.
What hobbies does he have? Maybe he feels like a "housewife" now he's retired and living alone, if he has no hobbies. If housewives aren't people he respects then, leaving aside his misogynistic attitude, that could be hard for him. Does he have an identity outside of his job or was his job everything? Has he lost himself now he's retired?
He can pay a cleaner, nobody gets those for free. He does need to treat the people who do it with respect though otherwise they'll drop him as a client. He'll need an agency to do a spring clean first, then a regular weekly clean to keep it nice. Ensuring it includes changing the bedding.
A trip to the doctor might help, although he's probably against antidepressants too and would see them as a sign of failure. Getting old and infirm can't be much fun, I'm sure a lot think they'd rather be dead and give up. If he wasn't depressed before living like this, he maybe is now. Unless he's always been a slob he won't be enjoying being one now. It's all very sad. He's obviously not coping if he was allocated carers, the council doesn't pay for those without good reason.
You can only help those who are willing to help themselves though. If someone is set on a path of self destruction there's not much you can do. Disengaging and stepping back is a better approach than becoming overly involved in someone's life when they don't actually want your help, that way madness lies and all you achieve is to hurt yourself.