There's relief in No 10 today after Theresa May and Jean Claude Juncker finally reached deal on the Irish border, EU citizens' rights and the so-called Brexit bill. The European Commission have subsequently recommended that 'sufficient progress' has been achieved in time for this month's EU council meeting – and that the Brexit talks should move on to trade in the new year. In order to get to this point, May has agreed a £40bn Brexit bill, time-limited ECJ role and a promise of no hard border between Northern Ireland and the republic.

However, for the government the hard work is only just beginning. The second round of negotiations is where the real battle will take place. It will mean that they can no longer fudge difficult issues and difficult decisions will have to be made over what sort of relationship Britain should have with the EU – importantly, whether the UK align itself closely to EU regulations or try and diverge. As the government reminds us frequently 'nothing is agreed until everything is agreed', when everything is eventually agreed, Parliament will be given a vote on whether to take the deal on the table – or reject it and leave the EU with 'no deal'.

So, who wants what – and who is willing to take a punt on no deal? Here is a run down of the Parliament's various Brexit tribes – from clean Brexit to no Brexit:

The 'no deal' Brexiteers

Numbers: 20

These are the people John Major would have called bastards. This portion of the Eurosceptic wing of the party have made it their life's mission to get Britain out of the European Union. It follows that they could put this before party. While they are open to negotiations with Brussels, their red lines are so uncompromising that it's hard to see how any deal agreed could be worth it. It follows that not only do they think 'no deal is better than a bad deal', they believe 'no deal' could be the best option as it would truly allow a clean Brexit.

Red lines: No ECJ jurisdiction, no payments to Brussels (unless a trade deal worth £40bn), an end to freedom of movement, no regulatory alignment – and exit from the customs union and single market.

Likely suspects: Peter Bone, Philip Davies, Bernard Jenkin, Jacob Rees-Mogg

The Bennites

Numbers: 10

Although the socialist wing of the Labour party is on the other side of the spectrum to the likes of Jacob Rees-Mogg, they can agree on one thing : the EU is bad. The hard Brexit socialists in the Labour party want a clean break that would see Britain leave both the single market and the customs union. They believe this is the only way to reset the dial and truly achieve a socialist Britain.

Red lines: exit from the customs union and single market.

Likely suspects: Dennis Skinner, Graham Stringer – plus John McDonnell and Jeremy Corbyn once upon a time.

The Vote Leave Brexiteers

Numbers: 80 - 100

The majority of Conservative MPs who campaigned for Brexit take a more, you could say, pragmatic approach to Brexit than their 'no deal' collagues. This is a group that likes to focus on the end point of the process rather than how you get there. It follows that their red lines are less stringent – they can deal with so many billion going to Brussels and the ECJ having a time-limited role, on the condition that when Britain does actually leave it is a proper Brexit.

Red lines: out of the customs union and single market, an end to ECJ jurisdiction. Important that Britain has the ability to strike free trade deals and diverge from EU regulations.

Likely suspects: Chris Grayling, Michael Gove, Boris Johnson, Dominic Raab

Blue Labour Brexiteers

Numbers: 90

This group of Labour MPs think it's vital that the concerns of working class voters in the EU referendum are recognised. It's made up of a combination of eurosceptic MPs and MPs who wish to represent their Leave-voting constituents. They all understand that for many of their constituents freedom of movement has disturbed the balance between capital and labour. It follows that they think Britain must leave the single market. They have seen what happened to Scottish Labour when they went against their voters on a referendum issue and they don't want the same thing to happen to them.

Red lines: an end to freedom of movement

Likely suspects: Frank Field, Caroline Flint, Johnny Reynolds, Stephen Kinnock

The 'stop banging on about Europe' group

Numbers: 150-250

Despite all the noise on Europe, a large chunk of the Conservative party (and a portion of the Labour party) is not ideologically opposed or attached to Brussels. This group is made up of some Cameroons who backed Remain to support David Cameron but aren't set on remaining. They would quite like to get some domestic policy agenda through – something that is near impossible when you're also doing Brexit. It follows that their mantra is whatever works. They are happy leaving the single market and customs union and having divergence if it looks like it will work. But if things start to look shaky, they could live with Britain having a soft Brexit with a Norway-style exit|

Red lines: No economic shock

Likely suspects: Nick Boles, Grant Shapps, Liz Truss

The Brexit mutineers

Numbers: 30 - 40

Dubbed by the Telegraph as the Brexit mutineers, this group of Tory rebels are pushing for the softer exit from the EU possible. They say they want to respect the result but point out that the terms of Britain's exit were never agreed. They think Britain ought to hug the EU once it leaves – meaning staying in the single market and customs union. This is the group that causes the government the biggest headache on a daily basis as they could team up with Labour to vote on amendments to try and soften the terms of Brexit.

Red lines: remain a member of the single market and customs union

Likely suspects: Dominic Grieve, Heidi Allen, Anna Soubry, Nicky Morgan and a number of Scottish Conservative MPs such as Paul Masterton.

Labour's single marketeers:

Numbers: 57

Without the Corbyn surge, these MPs would probably be in the shadow cabinet – and, subsequently, Labour's Brexit policy would be a lot clearer. They campaigned for Britain to stay in the EU and still think that this is the best option. If the UK can't do this, then the next best thing is to have as close a relationship to the EU as possible. Like the Tory mutineers, these MPs think that Britain must remain a member of the single market and customs union.

Red lines: remain a member of the single market and customs union

Likely suspects: Alison McGovern, Wes Streeting, Chuka Umunna (though at times he falls into the re-joiner category depending which Remain dinner he has attended)

The re-joiners

Numbers: 50-60

Forget talk about 'respecting the referendum result', this lot are more likely to say it was merely an 'advisory, non-binding referendum' that should subsequently be ignored. Rather than aim for a soft Brexit, Brexit ought to be stopped completely. When Britain leaves, expect them to campaign to re-join the EU.

Red lines: Leaving the EU

Likely suspects: The Liberal Democrats, the SNP, David Lammy, Clive Lewis, Ken Clarke