According to a joint investigation by The Mirror and The Observer, Boris Johnson’s top aide was seen in woodland near the Durham property he stayed at with his family on April 19, days after he was spotted back in Downing Street on April 14.
A number of Cabinet ministers had spent much of Saturday defending Cummings before reports of the second trip were published.
A Labour source said: “If these latest revelations are true, why on earth were Cabinet ministers sent out this afternoon to defend Dominic Cummings?
“We need an urgent investigation by the Cabinet Secretary to get to the bottom of this matter.
“It cannot be right that there is one rule for the Prime Minister’s adviser and another for the British people.”
SNP Westminster leader Ian Blackford said the adviser “must” be sacked.
The transport secretary also said restrictions put in place by the government on March 23 should only be followed “to the best of your ability” and that it was “up to the individual” to make decisions on how best to follow them.
From March 23 until the slight easing of the lockdown earlier this month, the government’s advice to the British public has been to stay at home for all but essential journeys such as food shopping or to buy medicines.