Downing Street has weighed in behind the health secretary, Matt Hancock, following a report that he is being lined up to take the rap for failures over protective equipment testing. Boris Johnson’s official spokesman said the prime minister has full confidence in Hancock and stands behind his pledge to get the UK to 100,000 coronavirus tests a day by the end of April, despite only 19,000 being carried out on Monday. However, a blame game has started in Whitehall about some of the problems that have dogged the government’s reaction to the Covid-19 crisis, with Hancock’s handling of the logistics around testing and personal protective equipment (PPE) under the spotlight. At the same time, some government sources have been pointing the finger at Public Health England for its sluggishness in increasing testing, and the NHS for failing to refer enough staff, which means completed tests are well below capacity of more than 39,000. With recriminations flying, Ed Davey, the acting Lib Dem leader, became the first politician to call for a judge-led public inquiry into the government’s actions after the pandemic is over, saying it “must have the strongest possible powers given the shocking failures on protective equipment for staff and the slow response of the government – to get to the truth and to give Boris Johnson the opportunity to answer the increasingly serious questions.” Tensions spilled into the open on Monday when an anonymous insider close to Downing Street told the Telegraph that Hancock’s 100,000 testing target was “made up”, and was an arbitrary figure that would “come back to bite him”. However, Johnson’s spokesman said: “An insider close to Downing Street is a new one on me. Whoever they are, and it could be anyone given that description, they are wrong.” He added: “We’ve said throughout that is a government target. We are working hard to hit it.” Johnson has previously set a target of 250,000 tests a day, without putting a date on it. A cabinet source said Hancock may have irritated some in No 10 and there had been tensions between him and Michael Gove, the Cabinet Office minister, in the “quad” of decision-making. But they questioned whether Downing Street would seek to make Hancock a scapegoat at such a crucial time, when he has such an important role in coordinating the government’s health response to the pandemic. Hancock also received backing from an unlikely source – one of his Labour predecessors, Andy Burnham, who is mayor of Greater Manchester. “I don’t agree with everything Matt Hancock has done but he has called some things right and I am certain he’s working flat out right now in the PM’s absence. With that in mind, this is an appalling move by Downing Street. It helps no one. Whoever’s responsible should be ashamed,” he said. Hancock, speaking at No 10’s daily press briefing, defended the UK’s response – and by extension his handling of the health department – saying the international comparisons about the spread of infections should take into account the size of the country. “At the start of this crisis, we said there were two absolutely critical tasks that formed part of the battle plan. One is that we got the exponential spread of this under control and brought the curve down. As you can see, that curve is now flat and that means we have achieved that objective,” he said. “The second thing we said is that we must do everything we can to make sure the NHS is not overwhelmed. We have achieved that because every single person who has needed treatment has been able to get that treatment … On those two core measures, the plan is working. “Does it mean every problem has been addressed? No of course not. I’ve gone through some of the details on PPE, where there are clearly challenges … But on the absolutely central core objectives, thanks to the work of the NHS, armed forces and many others, and people who have stayed at home, we have managed to bend down the curve and ensured NHS capacity is there.” He said he and his officials were looking every day at “how do you learn from where things are going well and where things aren’t going so well ... we are constantly looking around the world at these comparisons”.