The former Chancellor said he does not believe Mr Cummings’ trip to County Durham was “necessary or justified”, after the Prime Minister’s aide travelled 260 miles from London citing childcare reasons.
In a letter to constituents seen by his local newspaper, the Bromsgrove Standard, Mr Javid wrote: “Mr Cummings has argued he acted within the letter of the law.
“As a father myself, I also appreciate the fear and uncertainty one can feel when the safety of your child is potentially at stake.
“That being said I do not believe Mr Cummings’ journey to County Durham to isolate on his family’s estate was necessary or justified. I remain unconvinced his visit to Barnard Castle could be considered reasonable.
“I was also deeply concerned by his decision to return to Downing Street directly after coming into contact with a family member who was ill, potentially with coronavirus.”
The paper said Mr Javid, who quit as chancellor earlier this year following an escalation in tensions with Mr Cummings, wanted the senior adviser to apologise for the choices he made over lockdown.
At least 35 Tory MPs have called for Mr Cummings’ departure, while another former Cabinet minister, Penny Mordaunt, admitted there were “inconsistencies” in his account of what happened.
In an email to a constituent seen by the Press Association, the former Defence Secretary did not go as far as calling for Mr Cummings to leave, saying it is “a matter for the Prime Minister who he has as his adviser”.
However, she wrote: “Despite Mr Cummings’ statement yesterday (on Monday) I am personally still not clear of the facts.
"There are some inconsistencies in his account of events and the reasons behind it." “I am not clear about when he would have been symptomatic and on what dates he should have been in isolation. Or whether it was appropriate he drove home at the time he did.
“There is no doubt he took risks – refuelling at a petrol station is a risk to oneself and to others, which presumably he did.
“What is clear is that the scenes of the last few days will have undermined key public health messages. I deeply regret this and am very sorry for it.”
The Prime Minister has continued to stand by his trusted aide, insisting it is time to "move on" from the fallout amid plummeting poll ratings.
On Wednesday he rejected calls for Cabinet Secretary Sir Mark Sedwill to investigate Mr Cummings’ actions during the height of the coronavirus outbreak.
The divisive aide drove from the capital to his parents' property in County Durham to isolate with his family during the lockdown, and says he subsequently took a trip to Barnard Castle to see if he was fit to return home to London.
Mr Johnson came under intense questioning in an appearance before the Commons Liaison Committee of senior MPs, during which he announced NHS England’s Test and Trace programme would be rolled out from Thursday morning.
“Quite frankly I’m not certain – right now – that an inquiry into that matter is a very good use of official time,” the PM said. “We are working flat out on coronavirus.”
He said he was “deeply sorry for all the hurt and pain and anxiety that people have been going through throughout this period”, but repeatedly insisted it was now time to “move on”.
He argued during the appearance before the committee, comprised of the chairmen and women of Commons select committees, that the public wanted politicians to focus on “uniting our message” and “focusing on their needs”.
Mr Johnson also admitted it had been a “very frustrating episode”, which he sought to dismiss as a “political ding dong” with inaccuracies but he refused to state which aspects of the allegations were untrue.