They were discussing the Orlando shooting, which left 50 people dead and 53 hospitalised after a gunman identified as Omar Mateen targeted gay nightclub Pulse in Florida.
Jones stressed the importance of "calling out" the attack for what it was - a homophobic crime.
Omar Mateen, the man identified by officials as the gunman, stormed a gay bar in the early hours of Sunday morning. Following a three-hour hostage situation, he was shot by police.
The gunman’s father told US media that his son got angry when he recently saw two men kissing in Miami. He said that might be related to the attack.
Yet during Sunday's Sky Papers, journalist Hartley-Brewer and Mark Longhurst continued to equate the attack to that on the Bataclan, causing tensions to mount.
While discussing The Telegraph's front page, Jones pointed out that the Orlando attack is the biggest mass killing of LGB people in the West since the Holocaust.
He said: "People rationalise their hatred. This guy, apparently, according to his dad, saw two men kissing and he was repulsed by it.
"And people know this who are gay, that there are people out there who are sickened and repulsed by our very existence and this guy, however he dresses up his bigotry and hatred, is somebody who hates gays.
"He hates LGBT people and he had a gun... and he used that to murder LGBT people.
"But can we just be clear, because you say it's lunatics and the rest of it, if he went into a synagogue and killed innocent Jewish people... we call it out for what it is.
"This person is a homophobic terrorist, whatever else he is," adding: "At the end of the day this was a homophobic crime, as well as terrorism and it has to be called out."
Longhurst likened the attack to the Bataclan attack in Paris in November, saying it was an attack on the freedom of people trying to enjoy themselves.
Jones replied: "I'm sorry, but you just don't understand this because you're not gay."
Longhurst retorted: "Whether I'm gay or not has no reflection on the fact that this person killed 50 people."
The presenter then looked to tomorrow's Daily Telegraph headline, which read 'Isil wages war on gays in the West'.
He said: "Now you (pointing to Jones) share that view that basically this was deliberately targeted on one part of the community rather than the freedom to enjoy yourself no matter what your sexual orientation is?"
Jones: "What on earth, what are you talking about?"
Longhurst said: "I'm talking about the coverage in the newspapers. That's what we're here for."
Jones: "And I am trying to understand the point you're making. This was a deliberate attack on LGBT people in an LGBT venue. It was a homophobic terrorist attack. Do you not understand that?
"It's not an abstract, he just picked a random club out of nowhere. He picked a club because it was full of people that he regarded as deviants."
Hartley-Brewer responded by saying that the shooter would be as "horrified" by her as a "gobby woman".
Jones was visibly frustrated by the pair's comments and asked them why they were trying to "deflect".
He said: "I just find this the most astonishing thing I have ever been involved with on television."
As the discussion moved onto comments made by a spokesman from LGBT organisation, Stonewall, Jones said: "Oh, you're going to have an LGBT voice talking about it? Interesting."
Jones said: "I've had enough of this, I'm going home. Sorry."
People on social media were overwhelmingly supportive of Jones' stance.
Yet Hartley-Brewer was undeterred.
Responding to one person on Twitter who told the journalist to "stop trying to silence us as a community and start listening", Hartley-Brewer said: "Get a grip, love."
Labour MP Diane Abbott told her she was "in denial about the homophobic nature of the attack", to which Hartley Brewer said:
Hartley Brewer said Jones, whom she described a friend, had "plenty of time to have his say".
She added she said "absolutely nothing for which I need to apologise".
On Monday morning, Jones tweeted to say it was both "a terrorist attack and a homophobic attack on LGBT people - this really isn't hard".
He also called on people to attend a vigil tonight in Compton Street in London and urged people to stop berating Hartley-Brewer, saying the "none of the abuse directed at her is in my name".
Labour politicians, including two former candidates for the deputy leadership, backed Jones on the issue.
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