Ever since the government suffered a historic 230-vote parliamentary defeat on its draft Withdrawal Agreement (WA) in January, MPs, commentators and EU politicians have urged a cross-party consensus to solve the Brexit crisis.

Many observers believe that a parliamentary majority could exist for a soft Brexit by uniting moderate MPs in both major parties and leaving the backbench Conservative European Research Group in impotent opposition. Yet while this sounds appealing, it ignores fundamental attributes of Britain’s two-party system.

In two-party systems, policies that depend on temporary cross-party alliances may never emerge, even if they nominally command the support of a majority of MPs. That is because such alliances may cause deep-seated divisions in one or other existing party, weakening its internal cohesion.

The top panel of the diagram shows a two-party system in which the parliamentary strength of the two parties is indicated by the size of the boxes. Here, the centre-right party (B) enjoys a majority over the centre-left party (A) and forms the government.

Suppose a policy issue were introduced that internally divided each party’s ‘moderate’ MPs (those towards the centre of the diagram) from its respective ‘radical’ MPs.

Imagine further that a majority of MPs, drawn from each party’s ‘moderate’ wings, supported the policy and could pass a bill provided that they cooperated. This cross-party alliance is indicated by those MPs inside the dashed-line box.