Between July and September almost one in ten patients who attended A&E had to wait longer than four hours, according to The King’s Fund.
This is the worst performance for this time of year for more than 10 years, the think tank said.
Meanwhile 9.4% of patients waited longer than 18 weeks to begin hospital treatment, the worst performance since 2012, the report added.
And delays in discharging patients meant there was a significant rise in the number of patients trapped in hospital when they no longer needed medical treatment.
July to September saw a record high of 568,774 so-called “bed days lost” as a result of discharge delays - a 29% increase compared with the same quarter last year.
Many of these delays have been attributed to the struggling social care sector.
The new report also highlights growing pressure on GPs, who are treating more patients than ever before.
There was a 9.9% increase in the number of “patient contacts” with GPs in quarters one and two of 2016/17 compared with the same periods in 2014/15.
The think tank warned that rising demand was putting its services under “increasing pressure”, not just in general practice but across the health sector.
It is the first time GP activity has been included in The King’s Fund quarterly monitoring reports which highlight challenges facing the NHS.
The latest report also reveals problems with NHS finances.
This financial year has been billed by some as the “year of plenty” for the NHS, but many organisations have told the King’s Fund they do not think they will meet new targets set for them.
Nearly a third of NHS trusts are forecasting they will miss their “control totals” which are new financial targets set for each NHS organisation.
“The NHS is treating more patients than ever before, and these findings show that rising demand is putting its services under increasing pressure,” said Chris Ham, chief executive of The King’s Fund.
“The NHS needs to redouble efforts to manage demand and this will require investment in out-of-hospital services via the sustainability and transformation plans now being developed across England.
“The most pressing priority for next week’s Autumn Statement is to provide more funding for social care, following years of budget cuts.
“Not only would this benefit some of the most vulnerable people in society, but it would also help relieve pressure on the NHS.”
A Department of Health spokeswoman said: “The NHS is performing well despite the pressures of additional demand and an ageing population.
“Nine out of ten people are still being seen in A&E within four hours, and almost a quarter of a million more people were seen within four hours compared to last year.
“We are ensuring the money available to local authorities for social care will rise in the coming years - by up to £3.5 billion extra in 2020.
“We are also investing an extra £10 billion per year by 2020/21 to fund the NHS’s own plan for the future, helping to reduce pressure on hospitals with more help for GPs and mental health services.”