The high court has rejected a legal bid to challenge a decision not to investigate Dominic Cummings’s journey from London to Durham at the height of the first coronavirus lockdown. Max Hill, the director of public prosecutions, said any decision to investigate Cummings must be made by the police. He did not have the power to interfere. Martin Redston, a 70-year-old director of a London engineering firm, had sought a judicial review over the case. At a hearing in London on Tuesday, Michael Mansfield QC said Cummings “appearing to evade any genuine scrutiny for his actions due to government associations is undermining of respect for the rule of law”. Mansfield argued that as Hill had oversight of the prosecution system, he had a duty to “nudge” the police with advice, particularly over new legislation such as the coronavirus rules. In the Cummings case, he said Hill should have “stepped in with some friendly advice” following Durham Constabulary’s three-day investigation, which only examined Cummings’s movements in County Durham including a 52-mile round trip to Barnard Castle. Mansfield said: “He should have said to the Metropolitan police: ‘This is worthy of investigation in relation to the circumstances in which Dominic Cummings left his home … and whether this does constitute a reasonable excuse.’” He also said it was important for Hill to assert his independence from government after the attorney general and prime minister said Cummings had done nothing wrong. Mansfield argued there was a clear public interest in an investigation over a concern that “the lawmaker broke the law he has made or helped to make”, adding: “If there is a prominent member of government we say flagrantly not obeying them [the rules], this affects the level of security and health for the rest. The public would be reassured if they knew they had been properly investigated.” Duncan Atkinson QC, for Hill, argued the director of public prosecutions did not have the power to refer cases to the police. In any case, Hill had not made a decision not to prosecute, the court was told. “There is no decision that can be judicially reviewed,” he said. Permission to review was rejected. Lady Justice Carr, sitting with Mr Justice Picken, said: “The decision in principle is that this renewed claim for permission to apply for judicial review will be refused.” The reasoning for the decision will be set out later this week. Redston said he would consider an appeal. Speaking outside the court he added: “I’m very disappointed. The ultimate aim of this is to ensure that Dominic Cummings is actually prosecuted for the breach of lockdown regulations. So now we need to consider how we go forward.”