The work and pensions secretary had suggested the country’s ageing population and levels of obesity may be contributing to higher Covid-19 death rates.
But when Morgan suggested she was insinuating that the public was "too old" and "too fat", Ms Coffey replied: "I think that's a very insulting thing that you've just said."
He replied: “Well you just said it.”
The interviewer then asked her repeatedly to clarify what was “insulting” about his remarks.
Evading the question, Mr Coffey said: "I also have to point out that you started this interview late. Unfortunately I have to go to other broadcasters as well, and I wish we had more time."
⚡️ “DWP Secretary Therese Coffey 'walks out' on GMB interview”https://t.co/sy4PCspqg1
— Good Morning Britain (@GMB) January 25, 2021
Morgan responded: "I haven't interviewed you since May, so you can come back any time.
"It was you that boycotted the programme. Please don't play the 'we haven't given you enough time' card, because we gave you eight months and you didn't turn up."
The Tory MP replied by switching off her camera, saying: "I'm sorry Piers, I'm going to have to go to another broadcaster.
She continued: “You've already had 20 minutes of my time, I appreciate your time as well. Thank you. Bye bye.”
As the shot cut to Morgan and co-host Susanna Reid, the baffled presenter said: “Wow. OK. Thank you, Ms Coffey.”
He then continued: “She throws out two reasons why we have the worst death toll in the world, apparently: we have an ageing population – so we're too old –and we have an obesity problem – we're too fat.
"When I said, 'So it's the public's fault, is it? We're too fat and it's nothing to do with the government.' I was the one insulting?"