The PM's intervention comes as Grant Shapps, the energy secretary, admitted that delivering on Mr Sunak's five big pledges including the promise to stop the boats - will be "difficult".
Mr Welby raised eyebrows by attacking the Illegal Migration Bill as "morally unacceptable" last week, as the Bibby Stockholm barge set to accommodate 500 small boat migrants arrived in the UK.
But Mr Sunak fired back at the Church of England's most senior bishop and said more giant barges would be deployed, despite claims they amount to "prison hulks".
"I respectfully disagree with the archbishop on this and I've spoken about it a lot," the PM told the Mail on Sunday. "The number of illegal crossings last year was 45,000. That number has gone up four or five times in just a couple of years and it can't carry on like this."
He added: "I don't think it's right that the British taxpayers are forking out £5.5m a day to house illegal asylum seekers, that hotels in their communities are being taken over for this use. So barges are a solution to that and we will do as many as it takes."
Mr Sunak revealed he had put in place a new government committee structure which will see him chair regular meetings on the small boats crisis. "The moment that we have the green light we can crack on and deliver it," he said on the bill currently in the Lords.
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