I know just how you feel Rose21. My mum is 89 and has always been such a proud woman with a clean house. She is too proud to admit she needs any kind of help whatsoever. She certainly wouldn't pay a cleaner. Like your mum, we've noticed the house smelling a bit and food well past its sell by date in the fridge.
But like someone else suggested, my siblings and I work it between us. One will take her for a drive to a garden centre or somewhere else she used to enjoy and another will do a quick clean - we have to be careful not to remove things in an obvious way but we will go through the fridge and remove things that are clearly out of date and replace with fresh stuff and say - hey mum, I've bought you some cheese, you know the stuff you love and oh I've cleaned the cat litter tray out for ' the cat' (at the same time disinfecting all around etc). I never say its for HER lol - just the cat! (she loves her cat)
This does seem to work for us but am mindful that not everyone can even get to that stage.
Unless your mum makes herself ill as a result of poor hygiene then (as has been said) I doubt there is a lot you can do. It is still her life and her choice. I think sometimes people fear their independence being taken away from them so much and of course some of it could be depression or the onset of alzheimers.
I would try just doing bits and pieces such as cleaning the loo when you visit it, using anti bac wipes on the surfaces etc but without mentioning it.
My mum refuses to let anyone do her washing but she has now conceded she needs help changing her bed so I often, change the bed and pop the bedclothes in the washer without even telling her. I will just say as I am leaving - ohh the washers on mum, then run and leave her to it! She hasn't yet told me not to but...am waiting for it.
Good luck
I've got another 'keen'... Ouch!