In total 74% of Brits said they were concerned about a reemergence of COVID-19, with 21% saying they were very worried and 53% adding they were fairly worried.
The study showed 24% of people in the UK were not concerned about a new outbreak.
The prime minister announced on Tuesday restaurants, pubs, hotels and cinemas in England would be allowed to open from 4 July as the rate of infections and deaths continued to fall.
Johnson said the two-metre social-distancing rule would be replaced with "one-metre plus", which would facilitate the reopenings.
At Tuesday’s No 10 coronavirus briefing, both the government's chief scientific adviser Sir Patrick Vallance and the chief medical officer Professor Chris Whitty warned easing the restrictions would not be “risk-free”.
Prof Whitty said it was “absolutely critical” individuals and businesses take new guidelines seriously.
He said: “If people hear a distorted version of what’s being said, that says ‘this is all fine now, it’s gone away’ and start behaving in ways that they normally would have before this virus happened, yes, we will get an uptick for sure.”
Prof Whitty added the virus would likely to remain until spring next year.
The government has been warned it must be prepared for a second wave of coronavirus this winter, with health leaders adding urgent action was required to prevent deaths and protect the economy.
The presidents of the Royal Colleges of Physicians, Surgeons, GPs and Nursing – as well as the chairman of the British Medical Association, have written an open letter to all UK political parties,
The health leaders urged them to prepare for a second wave and called for a new cross-party commission to be established to develop solutions based on what we’ve learned so far.
They wrote: “While the future shape of the pandemic in the UK is hard to predict, the available evidence indicates that local flare ups are increasingly likely and a second wave a real risk.
“Many elements of the infrastructure needed to contain the virus are beginning to be put in place, but substantial challenges remain.
“The job now is not only to deal urgently with the wide-ranging impacts of the first phase of the pandemic, but to ensure that the country is adequately prepared to contain a second phase.”
Hairdressers, museums and art galleries in England will also be allowed to open from 4 July but other businesses which involve “close proximity” like nightclubs, soft play centres and indoor gyms will have to stay closed.