The report also included patient stories. In one, Arjun set out his experience trying to get support for depression and anxiety.
He did not want to take medication and it took him six months to convince his GP to put him forward for talking therapy. He then faced a further nine-month wait for treatment.
His mental health got worse and he started having suicidal thoughts.
Warnings were also made about hospital care, with the CQC saying there were ongoing concerns about staffing in maternity units in particular.
But it said there were some excellent examples of good practice and innovation too.
It highlighted a scheme in Haringey, north London, where GPs, community services, hospital staff and social workers had come together to identify and support local people with complex health conditions.
By providing extra tailored support, it managed to reduced emergency attendances and admissions in this group by 30%.
A Department of Health and Social Care spokeswoman said: "This report lays bare the scale of the challenge we inherited after years of neglect and underfunding."
But she said the government was getting the NHS "back on its feet", with extra investment beginning to help recruit more staff to key areas, such as GP services and mental health.
"We know there is much more to do – we are working at pace to fundamentally reform services through our 10-year plan to build an NHS fit for the future," she added.
But Dr Hugh Alderwick, of the Health Foundation, said the CQC was right to raise concerns.
"Over a year into the new Labour government, health and care services are still under massive strain."
He said the think-tank's own analysis suggested the government was still far from having a coherent policy agenda to make their promises a reality.
"A more concrete plan is now needed – including for rapidly testing and evaluating innovations that could improve local services."