Joining them in the studio was Stephen Doughty MP and former Brexit minister David Jones.
However, mid way through the conversation, Morgan went to put his point across to one of the guests, and Reid interrupted him, leaving him furious.
“Can I ask something,” Morgan began, “why the hell are we still talking about this Irish issue?”
“Because we didn’t talk about it enough before the referendum,” Reid interjected.
“Do you mind not interrupting me?” Morgan said, but Reid challenged him and replied: “Why not?”
Taken aback, Morgan stated: “Because I think it’s very rude.”
“It’s what you do all the time,” Reid pointed out, “I though I’d take a leaf out of your book,” she added giggling.
“And you always remind me it’s very rude!” Morgan remarked.
Keen to bring the conversation back to the debate, Doughty interjected and said: “Shall I, shall I interrupt you as well, we’re still talking about it because…”
However, Morgan took back control: “I haven’t finished my sentence so you can stop interrupting me as well.
“Here’s my point. Why are we still debating how these things work, two years after a referendum?
“I blame all the politicians here, for not actually thrashing all these issues out before people voted,” Morgan explained.
“Exactly, what I just said,” Reid commented.
Unable to resist bickering, Morgan replied: “Yes but I was about to say it.”
It comes after Prime Minister Theresa May is due to address EU leaders on her position in the negotiations ahead of the summit dinner in Brussels tonight.
However, May will be absent from the meal, as the leaders of the 27 nations staying in the EU following Brexit will be discussing the state of the talks.
It comes after May has had difficulty in negotiating the status of the border between Northern Ireland and the Republic of Ireland.
As following March 29 neat year, when Britain has left the EU, they intend to become the border between the UK an the EU.
Both sides have expressed the desire to avoid the border becoming “hard”, for example having checkpoints or other physical infrastructure to carry out checks on goods.
Nevertheless they are struggling to agree on how that should be done.
The European Council president, Donald Tusk, has said he had “no grounds for optimism” about the Irish border being solved at tonight’s summit.
He has also called on May to come up with ‘concrete proposals” to break the “impasse”.
The prime minister has told her cabinet a deal was within reach if the government “stand together and stand firm”.
And it seems she has the support from French finance minister Bruno Le Maire, who confirmed a Brexit deal was not far away.
In an interview with France’s Radio Classique he said: “We are not far from a deal.”
Good Morning Britain airs weekdays at 6am on ITV.