The NHS is the healthcare service of England, and is indeed responsible for public health, as well as providing general healthcare services. Public Health England is an executive agency of the Department of Health and Social Care which serves to advise the Government on public health matters, as well as being responsible for:
- making the public healthier and reducing differences between the health of different groups by promoting healthier lifestyles, advising
government and supporting action by local government, the NHS and the
- protecting the nation from public health hazards
- preparing for and responding to public health emergencies
- improving the health of the whole population by sharing our information and expertise, and identifying and preparing for future
public health challenges
- supporting local authorities and the NHS to plan and provide health and social care services such as immunisation and screening
programmes, and to develop the public health system and its specialist
- researching, collecting and analysing data to improve our understanding of public health challenges, and come up with answers to
public health problems
The bodies used to both fall under the NHS umbrella, but were split out into separate organisations in the Health and Social Care Act 2012 (explanatory notes).
Generally then, the NHS is ultimately responsible for providing and commissioning public health services in England, but will follow advice given by, and be supported by, Public Health England. PHE is more of a research and advisory organisation, and although it will work with the NHS to provide public health services, it isn't ultimately responsible for their provision.