To a leave voter it is a false choice to say we either sign the withdrawal agreement or we delay our exit from the EU. Neither of these is Brexit.

The prime minister seems to think if she keeps making that the choice, pro-Brexit MPs will eventually cave in and vote for her withdrawal agreement. As Keir Starmer tellingly said, the agreement stays the same, but the threats used, day-to-day and person-to-person, are different. The government has both told Labour they need to vote for it to avoid a no-deal exit – and told Conservatives they need to vote for it to avoid a delay or no Brexit at all.

The withdrawal agreement is incorrectly titled. It should be called the delay in leaving agreement, or the negotiation of a new partnership agreement. Its terms unite most remain and leave voters: remain voters say it is worse than staying in, as we have all the obligations without vote or voice. Leave voters rightly say it is not leaving, as the day after it is signed everything stays the same – save the loss of our places around the European council table and in the parliament.

We are ushered into a period of between 21 and 45 months of staying in the EU to try to negotiate a new relationship, against the pressure of knowing in the end we may have to stay in the customs union – with regulatory control of our markets from the EU for much longer, thanks to the backstop. We have given away most of our negotiating cards in the withdrawal agreement before the talks start.

The prime minister is now trying to negotiate some further extension – appearing to want just another short delay. She has two great worries about a longer postponement: the first is the UK would have to fight the European elections. Both Labour and the Conservatives could perform badly against the background of uniting to thwart Brexit – many leave voters could stay at home or find new pro-Brexit parties to support. The second worry is that she has no good reason to propose a long delay – she still seems to think that the only way forward is to sign the withdrawal agreement she accepted regardless of the disapproval of most MPs. The EU scarcely believed her last time when she said she could get it through the Commons by 29 March.

It is difficult to believe it is in the interests of either Theresa May or Jeremy Corbyn to reach an agreement to run the country as a grand coalition for the purposes of seeing Brexit through. Mrs May would lose the support of a significant portion of her parliamentary party and most of the membership in the process. If she adds either a customs union or a second referendum to the withdrawal agreement she would probably lose the majority of her MPs. Mr Corbyn could lose a good number of MPs if he agrees to help without securing both a customs union and a second referendum. His fairly astute party management on this most lethal of issues so far will be much more difficult if Labour is jointly responsible for the text of a new political declaration, and has to say fine words about a withdrawal agreement it has three times previously voted down.

Some MPs are prepared to choose between unpalatable options, as those who at the third time of asking voted for the agreement for fear of something even worse. This morning my colleague Bernard Jenkin understandably told the BBC’s Today programme a long delay might be preferable to the terms of the withdrawal agreement. I will continue to vote on the merits of the choices presented. If all the ones presented are bad I will vote against them all, as parliament did with a series of available options in the indicative votes. I still wish us to offer the EU a comprehensive free trade agreement and to leave on 12 April to start negotiating it.

• John Redwood is the Conservative MP for Wokingham