The coronavirus crisis led to a huge drop in the number of people who went to accident and emergency units in England last month compared to March last year, official data show.
At the same time, however, calls to the NHS 111 have risen to almost three million, double the same month in 2019.
Ministers say people should remain at home to stop the virus.
But the Health Foundation said it must still feel able to seek treatment for serious conditions.
"More work is needed to understand who does not attend A&E and whether unmet needs are being stored in the future," said Tim Gardner, senior policy member at the think tank.
There is also evidence that the number of people in hospitals in England suspected of having a heart attack has halved since the beginning of March – from 300 a day to 150.
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The British institution British Heart Foundation warned that thousands of people may be at greater risk of suffering heart damage in the long term.
"We have seen half of the patients we usually enter at our heart attack center at Imperial, some with significant delays," said Ramzi Khamis, consultant cardiologist and co-chief of cardiology at Hammersmith Hospital.
"Now we are getting very anxious about those we are not seeing, in addition to the delays."
NHS England National Medical Director Stephen Powis encouraged people to attend A&E "just like you always did" if they had symptoms of a stroke or heart attack.
Speaking at the Downing Street daily press conference on Wednesday, he said, "They are there for you, and while we are focusing on the coronavirus, it is important to stay focused on other emergency conditions."
According to NHS England numbers, there was a 29% drop in the number of people served in hospitals' A&E departments in March 2020 – around 1.5 million, compared to almost 2.2 million in March 2019
Emergency admissions also fell, dropping 23% last March, to almost 428,000.
Meanwhile, call the NHS 111 helpline – which was the first port of call for people with worsening coronavirus symptoms – soared
But despite the increase in the number of calls, 111 advised fewer people to attend A&E than usual and sent fewer ambulances than in March 2019.
"The NHS and the welfare system are making heroic efforts to respond to Covid-19's unprecedented challenge and this is having a dramatic impact on the way people seek care and the care being provided," said the Foundation Cheers.