The terse exchange took place on Euronews’ Raw Politics show, which is filmed in the Brussels building, after the two MEPs insisted the UK would negotiate a better deal due to member states’ collective Brexit fatigue. Mr Brok fired: “Do not misread the situation here. I’ve heard this too many times in the last three years.”
But Brexit Party MEP Diane James battled back: “I have to say you’re not on step here.
“Because if we get Merkel here and Macron also agitating then I think the opportunity for the UK is very, very positive indeed.”
Tory MEP John Procter weighed in after the studio descended into clamour: “The two facts that we are not in dispute over is that the people of the UK - the majority of them - want to leave the EU.
“And the remaining member states want us to leave as well.
“As do the MEPs here, because they don’t want Brexit to dominate their business for the next one, two of three years.”
Host Tesa Arcilla attempted to regain control, summarising: “So you think that would mean they would give you a better negotiating position?”
But Elmar Brok almost exploded with frustration, blasting: “Because you want to be out that would give you a better position?”
Heaving, he repeated incredulously: “Oh my god”, adding wearily “totally wrong”.
Downing Street has dismissed suggestions from Philip Hammond that the next prime minister might need another referendum to break the Brexit deadlock.
In a major speech on Thursday night, the Chancellor is expected to challenge Tory leadership hopefuls including Boris Johnson to set out a Brexit "plan B" and will suggest they may have to explore "other democratic mechanisms" to end the impasse.
But Theresa May, whose relationship with Mr Hammond has become increasingly strained, is firmly against a second referendum and believes "we should get on with delivering the verdict of the first one", a Number 10 spokeswoman said.
In a speech which will be delivered just hours after the final two names in the Tory leadership race are confirmed - with Mr Johnson almost certain to be one of them after opening up a commanding lead in the race - the Chancellor will warn that a no-deal Brexit could damage the economy and risk the break-up of the United Kingdom.
He will say that the £26.6 billion of "fiscal headroom" - which could potentially be used to increase spending or cut taxes - would be soaked up by a no deal Brexit.