A referendum may be needed to solve the Brexit impasse, but not the one #PeoplesVote want.

No deal, May’s deal, Norway plus, and a People’s Vote are all extremely unlikely to command a parliamentary majority before the 29th of March. With all sides doubling down and seemingly unwilling to compromise, the most feasible way out is a second referendum between May’s deal and no deal.

Following Tuesday night’s historic defeat on the EU withdrawal agreement, Theresa May has reached out to opposition parties and factions in parliament, asking to discuss a way forward.

All have obliged besides Jeremy Corbyn, who has refused to talk with Theresa May until she takes the possibility of a no-deal Brexit off of the table. Following Wednesday night, Theresa May has held meetings with leading figures in the SNP, Plaid Cymru, the Greens, the Lib Dems, the DUP, and groups of MPs from various factions in the Conservative party, including the ERG and the 20 or so MPs who seem determined to prevent a no-deal Brexit, led by former Attorney General Dominic Grieve.

While almost all sides have spoken optimistically about the chances of a new agreement being reached, none of them seems willing to compromise at all on the key issues, including the Prime Minister herself.

Despite May’s deal being rejected by an enormous margin of 230 votes, she seems convinced that if she goes back to EU negotiators and acquires some cosmetic changes to the backstop and perhaps more significant changes to the Political Declaration, she will be able to pick off enough Labour MPs to force her deal through the Commons. This is utterly delusional, even if she plans to run down the clock and increase the chances of a no deal. Such an approach may have had a chance of success if she had lost by a smaller margin, however with 116 votes to claw back it only displays complete ignorance.

If May agreed to add remaining in the customs union to her current deal, as the Labour Party would like, it may be able to get through parliament with Labour’s backing. However, May agreeing to this seems improbable at best. Such a deal would split the Conservative party and would risk bringing down the government if the hard-line members of the ERG, as well as the DUP, started a no-confidence motion as their last option, which explains why Corbyn remains strongly in support of staying in the Customs Union.

The remaining options are ‘Norway plus’, a ‘managed no deal’, and a second referendum, the question of which is debated.

A ‘managed no deal’ has no chance of getting through parliament, or receiving the government’s backing without the cabinet splitting in two. Although, the possibility of parliamentary deadlock leading to Britain crashing out of the EU without a deal on the 29th of March remains.

While Norway plus would allow the UK to strike free trade deals with countries around the world, providing the other countries in EFTA agreed, it would mean a much closer relationship with the EU than the EU Withdrawal Agreement in almost every aspect, most notably in the freedom of movement between EU citizens and the UK. Hence it would struggle to gain a majority in the Commons, as shown by a Lords amendment on the government pursuing a “Norway-style” relationship with the EU being defeated by 327 to 126 in June.

The chances of a second referendum with the option of remain getting through parliament are similarly low, as almost all Conservatives and all 10 DUP MPs would vote against, whilst the support for a people’s vote among Labour MPs is often overstated. Many, especially those who represent leave-voting constituencies and fear harming their chances of re-election, would vote against.

A second referendum between May’s deal and a no deal, however, would have a much greater likelihood of making its way through parliament, even if the 20-40 Conservative MPs who favour crashing out of the EU on the 29th of March vote against it. It would require an extension of article 50 until July (before the new European Parliament take their seats). However, this would almost certainly be agreed to by the EU and pass through the Commons.

With no-one willing to compromise, parliament is unlikely to agree to any feasible deal. We must let the people decide, whilst respecting the result of the first referendum.