With the balance of power now very fine, there are some obvious groups whose influence will strengthen in the coming weeks and months, and will seek to exert their influence on policymaking, both domestic and foreign, notably Brexit.  If a second election happens in the autumn, it’s fair to say that the various factions will want to do nothing to undermine their positions with their core constituencies, so expect milk and honey to be demanded by all.
Jeremy Corbyn and the Labour Party
The anti-Corbyn faction (ie, 75% of the 2015 Parliamentary Labour Party) have been silenced by their leader’s unexpected success.  Despite still only coming second by quite some way, the party is in triumphant mood and will undoubtedly be more united than it has been for much of Corbyn’s tenure.  This spells trouble for the Tories, who are always more ready to get rid of unsuccessful leaders and will inevitably look less united if they do.
But Corbyn still lost, and a further 3.6% swing is a big ask for a man carrying so much baggage.  His only hope is that Theresa May resigns, the Tories implode, and her successor feels she or he cannot not go to the polls to secure legitimacy.
So where will Corbyn seek to exert influence?  Expect continued opposition to an active foreign policy in places like the Middle East, and perhaps a moderating influence on Brexit (if his more pro-EU colleagues hold any sway in the coming weeks).  On domestic issues, the Tories are certain to be wading through Labour’s manifesto as we speak to find a softer more likeable version to put forward at the delayed Queen’s Speech; perhaps something stronger on workers’ rights, and a greater commitment to the NHS.
But the party will now be on election footing for the remainder of the year, so no tough decisions will be taken, and most Labour MPs will now fall into line behind their unlikely saviour.
Ruth and the Scots Tories
Small in number, the Scottish Tory contingent is greater than the sum of its parts.  The 13 MPs fought the election on a different prospectus to that which Theresa May put forward in England and Wales – no to indyref2 – and de facto answer to a different leader in Ruth Davidson.  On election night, they were the reason the Tories were not wholly glum; there is a sense they’ve saved the Union and that is altogether more important than anything else.  But Scotland also voted for a different Brexit outcome to England and Wales, and Davidson has lost no time in making clear what she thinks of the DUP’s views on social issues.
The Scottish Tories hold a special place in the heart of the party and what Ruth wants, Ruth often gets; just look at the moderation of policy in the Scottish manifesto on things like the winter fuel payments for the elderly and the return of onshore wind power.  If there is to be a moderation of Brexit, it will be because of the Scots, and by extension Nicola Sturgeon will also have some justification in believing the different vote of Scotland has saved Britain from the hardest form of Brexit.
Scottish Nationalist Party
Broadly speaking, it was a bad night for Scottish nationalism, though the party did retain a healthy number of MPs, albeit many of their returning members held on by the skin of their teeth and will be fearful of a second election at which many more will be sure to lose.  With that in mind, the hitherto lemming-like approach to loyalty of the party’s Westminster contingent may start to break down, making it harder for them to bargain with other parts of the House of Commons effectively.
The SNP’s principle that they will only vote on issues affecting Scotland has been found wanting, and so the rump grouping may become more active in the hope of demonstrating their effectiveness at opposing the Tories, since it’s clear that a Labour-voting Scotland might truly have stopped the Tories and Sturgeon will want to stop Scottish voters realising that.  Again, Brexit remains a key issue here, and it is one of the areas where she and Scottish Tory leader Ruth Davidson may have some shared ground.  If Sturgeon can moderate her position slightly she may effect policy at a UK level, but if she hasn’t learnt the lesson to resist her urge to make everything about independence, she’ll be a less influential piece of the Commons cake.
Democratic Unionist Party
The DUP MPs will undoubtedly receive a far greater degree of scrutiny than ever before under the arrangements to support the Tories, so their 10 strong number had better hope they’re as socially conservative in their private lives as they proclaim in their manifesto.  If they can hang together and work with the Tories – and the DUP are by no means sympathetic to all the Tories’ values – there could be a lot of pork for Northern Ireland in the form of infrastructure spending and additional money for Stormont when it gets back up and running.  On Brexit, they’re the one group who can be relied on to be broadly supportive of the Government’s approach to leaving the EU, probably even more so than the hard core eurosceptics inside the Conservative Party.
Remain supporting Tories
Never more important than right now, this small number could be the difference between the Conservatives remaining in power and being evicted.  To think that Theresa May is now reliant on the good will of the likes of Anna Soubry and Nicky Morgan, who wasted no time in saying she was a goner over the weekend, does not bode well for the Queen’s Speech.  Some humble pie, assurances around Brexit, and maybe a job or two, might be the order of the day to keep this gang in check.
The ‘awkward squad’
The right wing of the Tory party has never let winning elections get in the way of what they want; they have after all been very successful on things like renewable energy and Brexit.  Their number is probably greater than the Remain supporting Tories, but their views couldn’t be more divergent.  Quite how Theresa May plans to satisfy both these groups could be the headache of this Parliament, and the Whips’ Office in particular.  Clearly they will want to prevent backsliding on Brexit, and will share much in common with the DUP on social issues.  May will need to be careful not to let them get too much of a hook if she is to remain committed to the broad church approach – and broad church appeal – to governing.

H+K Public Affairs team – London