After Dominic Grieve’s amendment was passed in the Commons last week, Ms Cooper asked the Prime Minister whether she could confirm there will be a vote on statute before a withdrawal agreement is ratified.
Theresa May responded said there has to be an agreement before any withdrawal agreement bill can be put to MPs.
Ms Cooper, unsatisfied with the PM’s response, reiterates her question in a bid to find out whether MPs have a chance to discuss and debate the deal, or whether it will be a simple matter of voting for or against the bill.
The pair, speaking at a Liaison Select Committee meeting, also clashed over the Irish border issue, with Ms Cooper asking if the Government’s pledge that there will be no physical infrastructure rules out cameras being installed.
Mrs May responded: “We will be ensuring there is no hard border… that can be achieved in a number of ways,” but said she wouldn’t go into further detail.
Ms Cooper, unhappy with the PM’s answer, describes her comments as “baffling”.
The tense spat was the first real sign of life in an otherwise uneventful discussion and the exchange between the pair prompted a flurry of interest on social media.
One user joked: “Really getting into the xmas spirit watching the festive warmth between PM and Yvette Cooper.”
Another added: “Yvette Cooper is embarrassing herself repeating the same question because she doesn’t like the answer. She should clean her ears out. T May answered it several times.”
The clash comes exactly one year after a similar spat between the pair during the Prime Minister’s appearance in front of the Liaison Committee last year.
Ms Cooper had demanded more information about the Government’s EU exit strategy, but the PM refused to answer when she would release new Government plans for controlling migration.
Mrs May said: ”When we feel it is appropriate to give any indications of those details then we will do so.
“The objective of our Brexit negotiations will be to ensure that we get the best possible deal for the UK.”
“Which you have said many times…” Ms Cooper said irritably.
“And I will repeat,” the PM hit back.
Mrs May and Ms Cooper have a history of tense exchanges – the Labour MP shadowed Theresa May when she was Home Secretary under David Cameron.
She once labeled the government’s immigration vans urging illegal immigrants to go home a “divisive gimmick” in October 2013.