Ever since the government’s Brexit deal was voted down Theresa May and Jeremy Corbyn have been waiting for each other to expose their king chess pieces. For Corbyn that is May ruling out a no-deal Brexit or offering a permanent customs union to add to her withdrawal agreement.

If the prime minister were to make such moves then the ERG and many members of the cabinet would be incandescent with rage. Worse still, the DUP could deliver on the threat to terminate their confidence and supply arrangement with the Conservatives for ratifying a deal with a legally binding backstop. The government could then lose a vote of no confidence.

Corbyn exposing his king to May would be throwing his weight behind a second referendum. The Conservatives calculate that Corbyn supporting another plebiscite would damagingly divide Labour’s membership and lead to a backlash from many Labour MPs in Leave-supporting seats.

In lieu of either leader being able to claim “checkmate” – which few are holding out much hope for – the question is whether parliament can provide itself with a mechanism to wrest control of the Brexit process from the government.

Amendments to the government’s Brexit motion introduced this week aim to create several. The ones tabled by Yvette Cooper and Dominic Grieve in particular would even enable MPs to control the order of business in the Commons.

This control can be used to programme the passage of a piece of legislation, such as the bill Yvette Cooper introduced to mandate the government to seek a nine month extension to Article 50.

If a majority of MPs voted for such legislation then it could conceivably clear the Commons in a single day, just like the recent legislation on a budget for Northern Ireland. Importantly, the government would have no power to stop MPs advancing the bill in this chamber.

There have been interventions from people such as Jacob Rees-Mogg saying that the government could ask the Queen to prorogue parliament to stop Yvette Cooper’s bill in its tracks. There have also been suggestions that the Queen should be advised to block the bill’s Royal Assent.

These calls for an outlandish use of monarchical power are unnecessary. The middle of the bill’s passage – its stages in the House of Lords – provides a far easier opportunity to block it.

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Conventional wisdom suggests that the legislation would clear this chamber as rapidly as it cleared the Commons, given that most of its 800 members are opposed to Brexit. This is not the case.

The Lords is completely self-governing, and unlike those who sit on the green benches down the corridor its members can speak for as long as they like and filibuster to their hearts’ content. No guillotine motions can be introduced to silence a member or stop them from dancing on the Queen’s throne.

The Coalition government discovered this reality when Labour frontbenchers and crossbenchers in the Lords threatened to filibuster the legislation required to deliver the 2011 referendum on AV.

Peers know that normally it is futile to obstruct or talk out legislation that a majority in the Commons support. MPs could simply trigger the Parliament Act and bypass the Lords 12 months later, as Blair did over the banning of fox hunting. But a year is too long to wait given that the Article 50 clock runs out in fewer than 70 days’ time.

This poses the question of what the government might do if a bill it opposed were to end up in the Lords. Would ministers on the benches of the second chamber filibuster it? This would run contrary to Theresa May’s speech where she promised to respect the will of parliament after losing the vote on her Brexit deal.

Another option for the government might be to happily sit on its hands as proponents of Brexit in the Lords, such as Norman Lamont or Peter Lilley, obstruct all five stages of any legislation that doesn’t deliver on the 2016 referendum. They could even be encouraged to by ministers.