The pair were discussing whether Jeremy Corbyn should have a right to a vote on the issue, with Hartley-Brewer forcefully against the opposition leader having a say.
"I don't think Jeremy Corbyn should have a final say on whether or not we go to war - this is what we elect prime ministers to do. The Royal Prerogative allows it.
"David Cameron very foolishly allowed that [decision] to roll over to parliament - that's not what parliament is elected to do. This is not a time for committee debate," she said.
To which Jones retorted: "We're not in the United States, we're in Britain and we have a parliamentary democracy. One thing I support David Cameron on, and you don't hear me say that often, is giving parliament the decision."
Earlier on the programme Tory MP Bob Stewart made a fatal mistake during a rallying cry to rid the UK of Islamic State: "In the end, if our country is threatened by these bastards we've got to do something about it and that's what our armed forces are there to do," he said.
Presenter Ruth Langsford reacted with bemusement as Eamon Holmes urged those watching at home not to be offended by the swearing on the family-friendly show.
Stewart also hit out at Jones after the journalist described direct action in Syria as "a token British contribution."
The MP retorted: "Some might say it's more of a potent gesture" before telling Jones it's about our allied states. "It means so much if Britain join them, we need to join the game," he said.
The debate came as David Cameron is rallying to gain support for direct action against the Islamic State (IS), before a vote takes place in the Commons next week.