Labour leader Jeremy Corbyn on Tuesday. BEN STANSALL/AFP/Getty Images

Boris Johnson's bullish Brexit strategy has already led to a civil war within his Conservative Party, from which nearly two dozen more moderate MPs have quit or been expelled in a matter of days.

But things aren't much rosier in the opposition. Labour leader Jeremy Corbyn has long struggled to appease the Remain-backing will of most of his membership and lawmakers without causing fury in many of the party's Brexit-voting heartlands.

Those divisions were laid bare on Wednesday, when Corbyn's deputy, Tom Watson, said a second Brexit referendum should be held before a general election.

"Boris Johnson has already conceded that the Brexit crisis can only be solved by the British people," Watson said in a speech to the Creative Industries Federation.

"But the only way to break the Brexit deadlock once and for all is a public vote in a referendum. A general election could fail to solve Brexit chaos," he added.

That flies in direct conflict with Corbyn's message that there should be a general election as soon as a no-deal Brexit is taken off the table.

The position Labour would take in any second referendum is also anything but clear. Watson said the party should commit "unambiguously and unequivocally" to backing Remain, and several frontbenchers in the party have also made clear they would take that stance.

But Corbyn himself has not confirmed if he personally will campaign to remain, and confirmed in a speech on Tuesday that a Labour-forced second referendum would include a "credible" option for Leave on the ballot paper.

That credible option would likely be a Labour-negotiated deal, if the party were to win a snap election.

Labour's Shadow Brexit Secretary, Keir Starmer, attempted to downplay the divisions after Watson's comment. "At the moment there is a good discussion going on but we are very united having that discussion; we don't want to shut down discussion in our party," he said, according to Britain's PA news agency.

But it is difficult to ignore the bizarre optics that would likely unfold if Labour were to win a snap election: a Corbyn-led government agreeing a withdrawal deal with the EU, and then seeing several of its Cabinet members encouraging the public to reject that deal in a referendum in favor of the status quo.