I'm looking for legal and constitutional mechanisms that could prevent a hard Brexit, e.g. by keeping us in the Common Market. For example, could the Lords delay the triggering of Article 50 indefinitely? Or could the parliamentary vote result in a vote of no confidence in the government and subsequent election? More generally, how does one stop a British prime minister from making a bad decision?
The Prime Minister, Theresa May stated on 17/01/2017 that she wants a "hard" Brexit, including the UK leaving the single market and generally making a complete break with the EU.
What, if any, ways could this be stopped? By stopped I mean significantly softened or leaving the EU cancelled entirely. Failure to get the deal May wants and falling back to WTO rules would also be considered a "hard" Brexit in this context.