A consultation on what scale of sentence should be applied to the extended law will be carried out over the next few months by the Department of Health.
The move was one of the central recommendations of a review of patient safety commissioned by ministers in the wake of the Mid Staffordshire scandal.
It was led by Professor Don Berwick, a former adviser to US president Barack Obama, who said it was needed to targets the worst cases of a “couldn’t care less” attitude that led to “wilful or reckless neglect or mistreatment”.
The prime minister said: “The NHS is full of brilliant doctors, nurses and other health workers who dedicate their lives to caring for our loved ones.
“But Mid-Staffordshire hospital showed that sometimes the standard of care is not good enough. That is why we have taken a number of different steps that will improve patient care and improve how we spot bad practice.
“Never again will we allow substandard care, cruelty or neglect to go unnoticed and unpunished.”
He went on: “This is not about a hospital worker who makes a mistake, but specific cases where a patient has been neglected or ill-treated.
“This offence will make clear that neglect is unacceptable and those who do so will feel the full force of the law.”