Who’s the most important pro-European in the Labour party? The answer, of course, is Diane Abbott. The shadow home secretary is Jeremy Corbyn’s most committed ally, attends all of the crucial meetings where party policy is set, and is the least reconciled to Brexit of the party’s inner circle.

Mostly that importance matters due to her private influence and role in setting the party’s overall policy. But it’s also important in understanding the most significant exchange during her contribution to the debate on the withdrawal agreement in Parliament.

Assuming there is an early election – and one way or another it is getting harder and harder to see how this Parliament will last past April 2019 at the latest – one of the messages that the Conservatives will want to run with is that Labour wants to stop or to block Brexit.

There is a lively debate about whether that perception would help or hurt the Labour party, but we don’t need to get involved with that here: rightly or wrongly, the Labour leadership believes this perception would be deadly, and the Conservative high command agrees.

To hammer that message home, CCHQ will have lots of clips from relatively junior and obscure backbenchers. But to make it stick and to have any hope of getting purchase in voters’ minds, they will need something from a high-profile and significant figure on the frontbench, realistically one of the core three frontbenchers – Jeremy Corbyn, John McDonnell and Diane Abbott – who the Conservatives will most aggressively target in their adverts. They aren’t going to get it from Jeremy Corbyn, who is most comfortable when playing a Eurosceptic tune. They aren’t going to get it from John McDonnell.

That’s what was interesting about Abbott’s speech. She opened by saying that the Brexit vote was driven by a desire for greater sovereignty and by playing tribute to the late Tony Benn’s forceful arguments on that issue. The bulk of her response was devoted not to what Brexit means for migration, but the consequences of the withdrawal agreement on security and cross-border police co-operation: an area traditionally of Conservative strength that is compromised by the need to expunge the European Court of Justice’s jurisdiction over the United Kingdom. Asked if Labour would end free movement, she simply replied that yes: Labour’s manifesto recognised that as a matter of course, when the United Kingdom leaves the European single market, the free movement of people will also end.

Frankly, if the Tories are not going to get equivocation from Abbott, they are not going to find it elsewhere either. Another approach to “Labour will stop Brexit” may be needed.