Speaking during the prime minister’s appearance at the liaison committee on Wednesday, Cooper accused him of putting his “political concerns” ahead of public health messaging.
Johnson hit back, implying she was engaging in “political point-scoring” and insisting it was vital to move on from the controversy.
Cooper was unsatisfied with his response, saying she was unclear what the advice is to parents who have coronavirus and need to look after their child.
Cummings has said he travelled to his family estate in Durham out of fear he and his wife could not look after their son if they fell too ill, denying critics’ claims he broke and undermined lockdown rules.
Johnson and ministers have stood by the adviser, whom Tory MPs and opposition politicians have called on to quit or be fired.
The PM told Cooper that you should “take account” of “exceptional difficulties” in childcare, but Cooper insisted the difficulty was “very normal”.
She cited a Mumsnet survey that found today that a quarter of parents didn’t have access to local childcare when they had COVID-19, as Cummings said he didn’t.
“You need to be giving clear advice to parents,” she told Johnson.
The PM insisted that the “clear advice” is to stay at home unless you have to go to work or have “exceptional problems” with taking care of a child that “may cause you to vary your arrangements”.
She asked him about whether a parent with COVID-19 should stay put or follow Cummings’ example and travel for childcare.
“Here’s the problem, prime minister, the reason you are ducking this, the reason you are not giving people a straight answer, is because you are trying to protect Dominic Cummings,” Cooper said.
“The reason you have sent your all of your ministers out to say fudgy things and unclear things is because you are trying not to incriminate Dominic Cummings, and you don’t want to apologise for him.
“The problem is that means you are putting your political concerns ahead of clear public health messages to parents who have coronavirus.”
She added: “We need you to get this right now so can you tell us – you have a choice between protecting Dominic Cummings and putting the national interest first. Which will it be, prime minister?”
Johnson retorted: “My choice is the choice of the British people want us all to make, Yvette, that is as far as we possibly can to lay aside party political point-scoring and put the national interest first and to be very clear with the British public about what we want to do and how we want to take this country forward.”
He said their exchange had “illuminated why it is so important for us to move on” and said that when people “hear nothing but politicians squabbling and bickering, it’s no wonder they feel confused”.
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