The Department of Health is yet to respond to his views.
Prof Baker succeeded Sir Mike Richards overseeing the hospital division of the Care Quality Commission (CQC), having been his deputy since 2014.
The former hospital medical director said the NHS had not modernised because of a historic lack of investment.
He said: “One of the things I regret is that 15 or 20 years ago, when we could see the change in the population, the NHS did not change its model of care.
“It should have done it then – there was a lot more money coming in but we didn’t spend it all on the right things. We didn’t spend it on transformation of the model of care.”
The number of pensioners has increased by a third in the last 30 years and he said the system had not been able to deal with the increase in the number of elderly people in particular.
He also criticised accident and emergency wards and has written to all hospital chief executives calling for action to improve safety.
Too many hospitals had “wholly unsatisfactory arrangements”, he said, such as letting ambulances queue up at the entrance or leaving patients in corridors.
The CQC is expected to highlight increasing pressures on hospitals, who are in danger running out of beds and staff, in a report next month on the state of the health and care services.
That was an issue that Prof Baker touched on in the interview, saying: “Capacity is being squeezed all the time. That is a real concern going forward – because there comes a point at which the capacity isn’t there”.
The BBC’s health editor Hugh Pym said Prof Baker’s comments come after predictions of a difficult winter for the service, with the chief executive of NHS England warning of the possibility of a serious flu outbreak.
NHS Providers, representing trusts, has said that without an emergency cash bailout the service faces the worst winter in recent history, our correspondent added.