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Families hit with fines for leaving their home to seek childcare during the coronavirus lockdown could have their police fines reviewed, Matt Hancock has said.

It comes after Boris Johnson’s senior adviser Dominic Cummings sparked widespread public fury when it emerged he appeared to have flouted guidance and travelled to Durham in case he and his wife could not care for their four-year-old son.

Cummings is under pressure from Tory MPs to resign, but the prime minister has so far ignored the demands.

Hancock said on Tuesday the Treasury would “look at” reversing penalties for families after he was challenged by Brighton’s reverend Martin Poole at the Downing Street briefing.   

The health secretary said: “I will have to talk to my Treasury colleagues before I can answer it in full and we will look at it.

Hancock added the government would later “make an announcement from this podium” on what they decide. 

“We do understand the impact and the need for making sure that children get adequate childcare,” he said.

“That is one of the significant concerns we have had all the way through this.” 

Speaking to Sky News after the briefing, Poole said he challenged Hancock because he felt it was unfair some had faced fines when Cummings’ trip was deemed to be “exceptional”. 

He said “this is about unfairness”, adding: “I think people feel a very strong sense it is not right that certain people can behave in a way that the rest of us are not allowed to.” 

Shadow home secretary Nick Thomas-Symonds, meanwhile, said the question about a review of fines needed an answer from home secretary Priti Patel.

He tweeted: “Following today’s Downing St briefing it seems government will review fines issued during lockdown for travel to childcare. This is one of many questions that must be answered after guidance was undermined by ministers over the weekend. @pritipatel-I’d appreciate an urgent reply.”

The health secretary, who has been among those who have leapt to Cummings’ defence, was asked repeatedly about the adviser’s conduct at the briefing. 

He said he understood the “anger that some people feel”, adding: “I regret the anger that some people feel and Mr Cummings himself said that – with hindsight – he should have got all the facts out earlier.”