A diligent SW who compiles a tight Care Plan can make a huge difference.
So for example if Dad refused personal care in the mornings it was written into his plan that bed linen should be checked and bed made, dirty clothes/linen to be put out by the washing machine.
Lunch time, any spare time used to pop up to the shops for anything Dad wanted.
Tea time carers were to empty the kitchen bin and put dishwasher on.
Basically the SW filled the carers allotted time so they couldn't leave early if they had only done the basics.
I know it all depends on the time allocated for care for your Nan but try to make sure there are extra little jobs mentioned in the care plan.
Depending on the Agency your LA use, housework can also be factored in, think Dad used to get an extra 2 hours cleaning time one day a week.
Dads carers were wonderful, I bump into them in the village on a regular basis. They all remember him, and ask after him, not sure if that is good or bad.