Is it permissible to pay from one's zakat on money to patients of renal failure, cancer and other chronic diseases who need blood but cannot afford it, as the government health grants do not cover its cost?

It is permissible as long as the patients are incapable of covering the cost of their treatment. This is because the poor and the needy fall under the categories of zakat recipients; Allah Almighty says:

"Zakat expenditures are only for the poor and for the needy and for those employed to collect [zakat] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler—an obligation [imposed] by Allah. And Allah is Knowing and Wise."Al-Qur'an 9:60

The poor—and likewise the needy—are among those whose income does not cover all or some of their basic needs such as food and drink, lodgings, clothing and treatment.