Britain’s top public health leaders and scientists have warned Boris Johnson that trust in the government has been shattered by the Dominic Cummings affair and now poses real danger to life when lockdown measures are lifted this week. In a letter sent to No 10 on Friday, 26 senior UK academics and health administrators warn that public faith in the government is essential if the Covid-19 crisis is to be tackled effectively. However, they make clear that trust has been “badly damaged by the recently reported actions of Dominic Cummings, including his failure to stand down or resign in the public interest”, and by the prime minister’s refusal to dismiss him. In their extraordinary intervention, published in full in the Observer, the group also warns there has been a failure to set up an effective test, trace and isolate system to pinpoint and then quarantine newly infected people. As a result, they are now “very concerned for the safety and wellbeing of the general public” as the lockdown measures are relaxed. The warnings came as the government’s deputy chief medical officer Prof Jonathan Van-Tam went out of his way at the daily coronavirus briefing to make clear that people in positions of authority had a duty to lead by example and obey lockdown rules. In the clearest criticism yet by a top government figure of Cummings’ actions in driving with his wife and child from London to Durham in late March, Van-Tam said: “In my opinion the rules are clear and have always been clear. In my opinion they are for the benefit of all and they apply to all.” An Opinium poll for the Observer shows 81% of people believe Cummings broke the rules, and 68% think he should resign, including 52% of Conservative supporters. The poll, conducted on Thursday and Friday, also shows the Conservatives’ lead over Labour has crashed from 26 points at the end of March to just four points now. Last week alone the lead was cut from 12 to four points. Just days after the health secretary, Matt Hancock, unveiled the new test, trace and isolate scheme to combat Covid-19, the top health experts say the public mood is “too fragile to cope with another over-optimistic target-based strategy”, and urge transparency over timescales and risks for the national scheme. They say people need “to see with their own eyes that the necessary infrastructure and effective systems are put in place not just rapidly, but effectively”. They also say there is now a high risk of an uncontrolled spike in new infections, hospitalisations and deaths from Covid-19 over the summer. One of the letter’s main authors, Prof David McCoy, director of the centre for public health at Queen Mary University, London, described the test, trace and isolate system – which aims to quarantine people with Covid-19 and those who have been in contact with them – as “a mess”. “It is not a system,” he told the Observer. “It is just a fragmented collection of different programmes with nothing really holding them together. We needed to have spent much of April organising the test and trace programme and that was not done. We have wasted the time we had bought ourselves.” Part of that failure could be blamed on Dominic Cummings, he added. “Firstly he breached the lockdown rules but also as the chief adviser to the prime minister he has to take some responsibility for the failure of the government to make a proper response to Covid.” These experts’ concerns were also shared by other scientists who worry that daily rates of new cases are still too high to make test and tracing programmes feasible. Current infection rates suggest tracking operations will be quickly overwhelmed, they say. “The total number of cases a day is still substantial and there is evidence of decreasing compliance to restrictions and people moving farther away from their homes, increasing the chance of spread to previously unaffected areas,” said Prof Rowland Kao, at Edinburgh University. On Saturday night Rosie Duffield, MP for Canterbury, said she no longer a Labour whip after she met her partner while they were living separately, in breach of coronavirus restrictions. She met him for a walk when meetings of people from different households were not allowed. “My partner and I have been attempting to navigate a difficult personal situation as responsibly as possible. I apologise that during that process, we breached the guidelines,” she said. Oliver Dowden, the culture secretary, on Saturday announced plans to re-start competitive sport as the government maintained momentum towards easing the lockdown. Johnson has said that from Monday up to six people from different households can gather outdoors, including in gardens and for barbecues, so long as they keep 2 metres apart. Prof Devi Sridhar, also at Edinburgh University, said the current daily rate of thousands of new cases was unacceptably high. “Watching carefully what’s happening in east Asia and combining this with what we know so far about this virus, it does indeed feel like mistakes are being repeated,” she said. Daily new cases should be cut to double digits, or low hundreds at most, she said, while test, trace and isolate procedures are put in place and core infrastructure built up. Graham Medley, of the London School of Hygiene and Tropical Medicine, and a member of the government’s Sage scientific advisory group, agreed that the UK was taking a risk over the loosening of lockdown because of its current relatively high incidence of infections. “There is less room for mistakes,” he added. “The precautionary principle suggests that if you are unsure about the risks, especially when the outcomes have a large impact, then you should err on the side of caution.” Four other members of the Sage committee, Prof John Edmunds, Sir Jeremy Farrar, Prof Calum Semple and Prof Peter Horby, all warned on Saturday that the government was taking a serious risk by easing the lockdown while 8,000 people a day were being infected. The number of people who have died from Covid-19 in all settings rose on Saturday by 215 to 38,376. A further 2,445 people tested positive for the virus.