There are vacancies for up to 100,000 doctors and nurses across the NHS, undermining attempts to hit waiting time targets.
The staff shortages raise questions about whether it is possible to deliver genuine improvements in outcomes as well as recover waiting times, even with a funding deal worth up to £20bn a year announced last month by the prime minister.
Simon Stevens said the NHS could deliver improvements in both access and outcomes, but that staffing was central to its prospects of success.
The 3.4% annual increase comes after eight years of austerity funding that has left more than four million people waiting for operations and seen the worst ever A&E performance against modern targets.
The prime minister has demanded that the NHS recover those targets, as well as delivering improvements in cancer outcomes, which are below the European average for some common cancers, and increasing mental health provision.
Mr Stevens said it will be possible to address both access and quality of care, despite scepticism from hospital chiefs, economists and health think tanks.
“We want to make sure that as we put extra money in it is used wisely.
“But looking out at cancer care for the next decade, if we can focus particularly on early diagnosis, getting checked out soon, we are going to have an impact on cancer survival.
“We want to keep short waits for A&E care and planned surgery, but we want to make big improvements in cancer care and unaddressed areas such as in mental health services, and to do that we are going to need more staff.
“We have got five new medical schools coming on line but it takes 10 to 12 years to train a doctor, and we need to look after the ones we have, because we have a million and a half of the best people in the country.”
Mr Stevens also wants greater protection for existing staff, calling for automatic prosecutions and stiffer sentences for anyone who attacks NHS workers.
“Too many of our paramedics, nurses, A&E doctors, say they are on the receiving end of assaults and violence from the people they are trying to look after,” he said.
“I think it is time to say that if you beat up an ambulance crew you should expect to be prosecuted, and if there needs to be changes in the law to make that clearer to everybody, we should fully support them.”
Mr Stevens insisted that despite continued debate about the sustainability of the NHS’s funding model and the principle of universal access, the government’s position means the fundamental contract between the health service and the citizens it serves would continue.
“The range of health services offered will continue to expand, the way we interact will change, but fundamentally the deal is that we as citizens and taxpayers of this country fund a service that will be available for us when we need it and that is going to endure,” he said.
The 70th anniversary of the foundation of the NHS on Thursday will be marked by services at Westminster Abbey and York Minster attended by staff, patients, members of the Royal Family and government.
The Countess of Wessex will attend the Westminster Abbey service, at which speakers will include health and social care secretary Jeremy Hunt, and Manchester bombing survivor Freya Lewis.