The coronavirus crisis led to a huge drop in the numbers of people going to accident and emergency units in England last month compared with March last year, official figures show.
At the same time, though, calls to NHS 111 rose to nearly three million, twice as many as in the same month in 2019.
Minsters say people must continue to stay at home to stop the virus.
But the Health Foundation said they should still feel able to seek treatment for serious conditions.
"Further work is needed to understand who is not coming to A&E and whether unmet needs are being stored up for the future," said Tim Gardner, senior policy fellow at the think tank.
There is also evidence the number of people seen in hospital in England with a suspected heart attack has halved since the start of March – from 300 per day to 150.
'There for you'
The charity British Heart Foundation has warned thousands of people may be at greater risk of long-term heart damaged as a result.
"We have seen about half as many patients as we usually do coming into our heart-attack centre at Imperial, some with significant delays," said Dr Ramzi Khamis, consultant cardiologist and co-head of cardiology at Hammersmith Hospital.
"We are now becoming quite anxious about the ones we are not seeing, as well as the delays."
NHS England's national medical director, Stephen Powis, encouraged people to go to A&E "just as you always have done" if they had symptoms of a stroke or a heart attack.
Speaking at the daily Downing Street press conference on Wednesday, he said: "They are there for you and, although we are focusing on coronavirus, it's important we continue to focus on other emergency conditions."
According to NHS England figures, there was a 29% drop in numbers of people attending hospital A&E departments in hospitals in March 2020 – about 1.5 million, compared to nearly 2.2 million in March 2019
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