The UK parliament of 2017–2019 had to decide what form of Brexit, if any, it would accept in the government’s negotiations with the EU over a withdrawal agreement. Despite a large majority of MPs having supported Remain in the 2016 referendum, with most opposed to a ‘hard’ Brexit of looser ties between the UK and the EU, all attempts to pass a ‘soft’ Brexit failed. The final withdrawal agreement reflected a hard Brexit that was closer to the preferences of a 28-strong group of Eurosceptic Conservative MPs than to those of any other party or faction in a 650-seat parliament. This article identifies the two-party system for government as a crucial variable in explaining this unexpected outcome. Governments seek majorities from among their own MPs rather than relying on the uncertain support of the opposition. This not only makes party cohesion vital, but also creates leverage for organised factions to hold sway.