The director of public prosecutions, Max Hill, is being threatened with legal action over the failure to investigate Dominic Cummings for alleged breaches of the lockdown rules. A legal team, headed by the barrister Michael Mansfield, has twice written to Hill, expressing concern that no action has yet been taken against Cummings after a Guardian and Daily Mirror investigation revealed the prime minister’s chief adviser travelled with his family to Durham and Barnard Castle during the lockdown. The letters were sent on 3 and 8 June on behalf of Martin Redston, a 70-year-old London engineer who is concerned that the lockdown laws should apply to everyone irrespective of their position in government. Replying to Redston’s second letter, Hill’s office confirmed his complaint had been passed to a special crime division of the Crown Prosecution Service (CPS) and a full response would follow in “due course”. But it stopped short of saying the matter was being actively considered, as requested by Redston’s legal team, which also includes the firm Hackett & Dabbs. In a new letter to Hill sent on Tuesday, Redston’s lawyers claim the failure to provide a substantive response were grounds for a judicial review. And it threatened to begin proceedings if no action is taken by Hill by 4pm on Thursday 11 June. The letter said the demand for urgency was “proportionate” given “a very serious loss of public confidence in the due process of the rule of law” at a time of a continued public health emergency that requires public compliance. It also warned any delay risked losing evidence such as CCTV footage and credit card records relating to Cummings’ movements in the north-east. The letter also pointed out that in his statement from the rose garden of Downing Street, Cummings admitted returning to work at No 10 on 27 March after tending to his wife who was displaying symptoms of coronavirus. He then admitted travelling to Durham with his wife to seek childcare for their four-year-old son, the letter pointed out. A spokesman for Hill and the CPS said: “We have responded to the letter today referring those involved to the relevant police force as investigating alleged offences is a matter for the police not the CPS.” Redston’s lawyers point out that under the CPS’s own policy it may receive an allegation of an offence from a member of the public and can refer such cases to the police. Redston, whose complaint is being funded by donations to Crowd Justice, said: “The prime minister was absolutely unequivocal when he said people needed to ‘Stay at home, Protect the NHS and Save Lives’. The rules were entirely clear and should apply to everyone.” He said he was prevented from attending a friend’s funeral due to the lockdown restrictions. And he has also been unable to see his grandchildren since the start of the outbreak. After recovering from coronavirus, Cummings admitted travelling to Barnard Castle with his family on 12 April to test his eyesight. An initial three-day investigation by Durham police into Cummings’ travels found that he might have breached health protection regulations when he took a 52-mile round trip to the town. But it said Cummings’ 516-mile round trip from London to Durham and back had not broken health protection regulations. The force decided to take no further action after making no finding in relation to “stay at home” government guidance. On Sunday, a separate campaign for a new investigation into Cummings over alleged breaches was launched, by lawyers with the backing of health workers and some families of coronavirus victims. • The headline of this article was amended on 11 June 2020 because an earlier version referred to the director of public prosecutions as the “UK’s top prosecutor”. The position relates to England and Wales, not the UK.