Hi Ben, welcome to the forum. I can't give you a straight answer to your question, I suggest you take advice from Shelter and/or the CarersUK helpline. However, I'm a great believer in the saying "There's more than one way of killing a cat" (with apologies to cat lovers everywhere).
Whilst you may not be entitled to full Housing Benefit, there may be other ways of boosting the overall income of the household, and therefore be able to "top up" your rent yourselves.
In order to keep our replies as relevant as possible, it would help if you could give a bit more information about your situation. No need to answer any you are uncomfortable about.
Can I ask where granddad has gone? How old is grandmother? What is the nature of her illness, so that you need to care for her full time? When did she last have a Social Services Needs Assessment (if ever?). When was your last Carers Assessment?
Have you claimed Carers Allowance and Employment Support Allowance?
Finally, when your gran passes away, will you "inherit" any right to housing?
One of the problems with things like housing is that there is a "domino effect". So the more benefits Gran gets from DWP, the more benefits you are entitled to, and there's a knock on effect on Housing Benefit.
In addition, if Gran's Needs Assessment shows she needs help, then under certain circumstances Social Services can pay you, or someone else, to look after her.