Ahead of the Prime Minister's appearance, Liaison Committee chairman Sir Bernard Jenkin told the PA news agency: "I have got no intention of preventing any subject any member of the committee wants to raise".
Both Cummings and the Prime Minister had repeatedly insisted he did nothing wrong by driving from London to Durham in late March, nor by visiting Barnard Castle in mid-April on their way back to London.
At least 35 Tory MPs have called for Mr Cummings' departure, while senior minister Penny Mordaunt admitted there were "inconsistencies" in his account and that "there is no doubt he took risks".
Sajid Javid, who resigned as chancellor in February after Mr Johnson ordered him to fire his team of aides, also called on Mr Cummings to apologise.
Mr Johnson said the "heroic efforts" of NHS workers and the public mean that the first test of protecting the NHS's ability to cope has been met.
On Tuesday, junior minister Douglas Ross resigned in protest at Mr Cummings' defence of his behaviour, saying that his interpretation of the government guidance was "not shared by the vast majority of people". "We are working flat out on coronavirus".
'My personal hope is that as we make progress in getting the virus down ... we are going to be ready to scale back that distance which I feel will be notably precious on (public) transport and within the hospitality sector, ' he added.
"I know that for many people this will be a long-awaited and joyful moment", he added.
While Mr Johnson was taking part in a video conference with the panel of senior MPs, Conservative MP Giles Watling tweeted: "I've been listening to the PM in the Liaison Committee".
It comes as the test and trace system has been launched today (Thursday) despite delays in rolling out the coronavirus app - being trialled on the Isle of Wight - across the country.
Mr Cummings said he drove to Durham to isolate in a property on his father's farm because of concerns over care for his four-year-old son if both he and his wife were incapacitated by Covid-19.
Tory MPs and scientists advising ministers have warned that Mr Cummings' actions risk undermining respect for the restrictions which have helped curb the spread of the virus.
He has received the continued support of the prime minister, who said that his aide had acted legally and with integrity.
This was Mr Johnson's first appearance before the committee since he became PM last July.
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More than 4.75 million people have been reported to have been infected globally and 314,414 have died, according to a Reuters tally.