In an open letter published in the British Medical Journal, ministers were warned that urgent action would be needed to prevent further loss of life. The presidents of the Royal Colleges of Surgeons, Nursing, Physicians, and GPs all signed the letter. It comes after Boris Johnson announced sweeping changes to England's lockdown. The Department of Health said it would continue to be guided by the latest scientific advice and would give the NHS "whatever it needs".
On Tuesday, the prime minister said pubs, restaurants, cinemas and hairdressers will be able to reopen from 4 July.
The 2m social-distancing rule will be replaced with a "one-metre plus" rule, meaning people should stay at least 2m apart where possible, but otherwise should remain at least 1m apart while taking steps to reduce the risk of transmission, such as wearing face coverings.
The 2m rule will remain in Scotland, Wales, and Northern Ireland, however.
Both the government's chief scientific adviser Sir Patrick Vallance and the chief medical officer for England Professor Chris Whitty stressed Mr Johnson's plan was not "risk-free" at Tuesday's final daily Downing Street coronavirus briefing.
Following the prime minister's announcement, health leaders called for a "rapid and forward-looking assessment" of how prepared the UK would be for a new outbreak of the virus.
"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," they wrote in the letter.
"Many elements of the infrastructure needed to contain the virus are beginning to be put in place, but substantial challenges remain."
The authors of the letter, also signed by the chair of the British Medical Association, urged ministers to set up a cross-party group with a "constructive, non-partisan, four nations approach", tasked with developing practical recommendations.
"The review should not be about looking back or attributing blame," they said, and instead should focus on "areas of weakness where action is needed urgently to prevent further loss of life and restore the economy as fully and as quickly as possible".
Former Conservative health secretary Jeremy Hunt told BBC Radio 5 Live's Emma Barnett that he did not think it was the right time for a public inquiry, which would take up a lot of ministerial time but he thought there was a "very real risk" of a second wave.
"You just have to look to Germany, which has had one of the best responses to the pandemic and they have got this big issue at a meat processing plant with thousands of people infected; look at South Korea which had to trace the contacts of 1,700 people after a nightclub incident - that's another country which has had a very good response to coronavirus," he said.
"In the places which are the best in the world they are dealing with these spikes and we have to recognise there is a very real risk of that here too."