Ministers and the NHS have pushed back strongly against a series of reports alleging splits within the government and between ministers and health bosses over the response to coronavirus, insisting talk of tensions is wildly overblown. Following claims of disagreements between the Department of Health and Social Care and both NHS England and Public Health England (PHE) over difficulties in rolling out more tests for the virus, the health service took the unusual step of calling the reports “factually wrong”. Meanwhile, Matt Hancock, the health secretary, dismissed the idea that he and the chancellor, Rishi Sunak, had disagreed over when to end the lockdown. The reports capped a difficult week for the government after criticism over the slow pace of testing and the provision of protective equipment for NHS and care staff. The nadir came on Wednesday when a stumbling performance by Alok Sharma, the business secretary, prompted even some loyal newspapers to lead their next day’s editions with talk of chaos. The following day Hancock emerged from seven days of isolation because of coronavirus symptoms to pledge that 100,000 tests a day would be carried out by the end of the month, a target he conceded on Sunday would be hard to achieve. In a story alleging widespread splits within government and between ministers and various agencies, the Sunday Times said ministers were blaming NHS England and PHE over the delays in supplying protective equipment and for taking an over-centralist, controlling attitude towards private laboratories helping with tests. NHS bosses are believed to be particularly annoyed at the claim they are unwilling to work with the private sector, pointing to a deal made last month to work with private hospitals to share the burden. An NHS England spokesman said the claims were “factually wrong”, saying NHS hospital labs had done the testing they had been asked to do, focused on patients and staff, and that mass testing would always have needed outside help. NHS England “has itself rapidly engaged with the private sector in areas for which it has responsibility, as evidenced by a deal to redeploy almost all independent hospitals across England to help with the expected surge of coronavirus patients”, the spokesman said. “This means another 20,000 staff, 8,000 more beds and an extra 1,000 ventilators can all be used in this battle.” They added: “The NHS in partnership with the military has acted in record time to establish new Nightingale hospitals in London and now in four other regions across the country. Everyone across the NHS is completely focused on coming together to respond to the biggest global health emergency in a century.” A separate report in the Mail on Sunday said Sunak had made “robust” arguments to Hancock about the economic need for a relatively swift return to normality, with unnamed critics telling the paper that the health secretary had misjudged the balance between the NHS coping with coronavirus and the wider needs of the economy. Asked on Sky’s Sophy Ridge on Sunday show whether he had fallen out with the new chancellor, Hancock said: “No, we’re working very closely together and what matters is that we can get out of this as fast as possible.” Hancock added: “I think that Rishi is doing an absolutely brilliant job as chancellor, the measures that he’s put in place to support businesses, to support people, self-employed people and employed people are absolutely phenomenal, and in fact he has been lauded around the world for the first-class economic response we have got in this country.”