Dr Wollaston later raised a point of order in the House of Commons to brand the prime minister’s action “entirely unacceptable”.
Deputy Speaker Lindsay Hoyle responded: “You have to hold all offices – and even the prime minister – to account, I recognise that.
“I do also recognise it’s very difficult times at the moment.”
Labour’s Yvette Cooper, the chair of the home affairs select committee, said: “At such a time when there are so many important decisions to be made for the country, surely it is utterly irresponsible for the prime minister to refuse to answer detailed scrutiny questions from the committee.”
She also questioned whether the committee could trust Mr Johnson’s promise to meet them in December or January, as he has already postponed his appearance three times.
But Conservative MP Sir Patrick McLoughlin, another member of the liaison committee, defended Mr Johnson.
“The prime minister is held to account by all MPs every week for over an hour,” he said.
“As far as people not being held to account, it is simply not true of the prime minister.”