Mr Carswell, who quit as Ukip’s only MP over the weekend, claimed he wanted to “allow people to have control over their money” by opting out certain public services – such as education and healthcare.
Boulton was left enraged by the politician’s comments, berating him for comments he has made in his new book during the heated debate.
Outlining his plans, Mr Carswell told Sky News: “At the moment, we have created a system where pets often get better primary care than people.
“When a person wants primary care they have to stand in line and wait because there is a monopolistic system…”
Adam Boulton berated Douglas Carswell over his plans for NHS funding
That is a slogan! You are talking about dismantling the NHS
The veteran news host swiftly interjected, he blasted: “That is a slogan! You are talking about dismantling the NHS.”
Allowed to continue, Mr Carswell added: “I’m talking about allowing people control over their money – it’s their money, Adam.
“The idea that politicians know best is the problem.”
Boulton moved on to suggest families who send their children to “private schools” could abuse the system by choosing to opt out of funding public facilities instead of putting the money towards private institutions.
Mr Carswell replied: “I never said in the book it should be used as a subsidy for public schools.”
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The now independent MP for Clacton is now subject to calls from the Tories to rejoin the party, having sensationally defected to Ukip in 2014.
Andrew Bridge, Conservative MP for North West Leicestershire, told The Telegraph: “Douglas Carswell should return to the Conservatives after a period as an independent – he needs to rebuild a relationship with his local Conservative association.
“On the matter of whether he should return to the Conservatives, I don’t think he should have ever left.
“If we punished every politician who made a mistake we would not have many politicians.”
Shocking charts show the NHS could be in crisis Thu, February 9, 2017
Do these charts prove the NHS is in trouble?
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During an interview on ITV’s Peston on Sunday, Mr Carswell refused to rule out a return to his former party. Asked how he would respond from an approach from the Clacton Conservatives, he said: “Right now, thanks but no thanks.”
Former Ukip leader Nigel Farage has demanded Mr Carswell call a by-election having left the party.
Mr Farage said he had campaigned to allow constituents to recall MPs and trigger by-elections and must be held to that.
He said: “He has now given up the label on which he voted in.”