At the daily Downing Street press conference on Sunday evening, Boris Johnson said Dominic Cummings had "acted responsibly, legally and with integrity" by driving 260 miles to County Durham to isolate due to childcare concerns.
But writing on Twitter near the end of the briefing, The Rt Revd Nick Baines, Bishop of Leeds, said: "The question now is: do we accept being lied to, patronised and treated by a PM as mugs?
"The moral question is not for Cummings - it is for PM and ministers/MPs who find this behaviour acceptable.
"What are we to teach our children? (I ask as a responsible father.)"
A few minutes earlier, the Rt Revd Dr Helen-Ann Hartley, Bishop of Ripon, commented in response to a critical tweet about the Prime Minister.
She wrote: "Integrity, trust and leadership were never there; just a driven misguided ideology of power that has total disregard for the most weak and vulnerable, and those who work to protect and care for us with relatively low pay."
Dr Hartley also shared some details of her experience of being unable to see her parents during lockdown.
She tweeted: "My parents live in Durham, an hour away from where we live. My father finished radiotherapy treatment just before lockdown.
"I've missed his birthday, Mothering Sunday and countless other catch-ups that would have happened.
"And that's a fraction of a story compared with others."
Meanwhile, the Rt Revd Vivienne Faull, Bishop of Bristol, tweeted after the Downing Street briefing: "#livingdifferently in a nation where the PM has no respect for the people.
"The bonds of peace and our common life (which had been wonderfully strengthened during the testing by CV-19) have been dangerously undermined this evening."
In an apparent reference to US President Donald Trump, The Rt Revd Pete Broadbent, Bishop of Willesden, also tweeted on Sunday evening: "Johnson has now gone the full Trump."
Later on Sunday night, The Rt Revd Dr Pete Wilcox, Bishop of Sheffield, commented on Twitter: "I don't usually tweet politics, and I have carefully steered clear during the pandemic. But tonight I must say: the PM & his cabinet are undermining the trust of the electorate and the risks to life are real."
The Rt Revd Dr David Walker, Bishop of Manchester, appeared to question how the Church of England could work with the Government during the coronavirus crisis.
He wrote on Twitter on Sunday: "Unless very soon we see clear repentance, including the sacking of Cummings, I no longer know how we can trust what ministers say sufficiently for @churchofengland to work together with them on the pandemic."
Commenting on Mr Baines's earlier tweet, The Rt Revd Olivia Graham, Bishop of Reading, wrote on Twitter: "I find myself deeply worried by the PM's judgment call on this one.
"Not from a political perspective but a moral one.
"His response lacks both integrity and respect and he has just made his task of leading us through this crisis much, much harder."
The Rt Revd Christine Hardman, Bishop of Newcastle, also wrote on Twitter that she had been left "deeply troubled tonight" after the Prime Minister's briefing.
She added: "We can forgive mistakes and poor judgement and can understand and admire loyalty but forgiveness and understanding need openness and we did not see this tonight."