Here are some of the coalitions or arrangements that could result. Most scenarios are either unlikely or would be extremely fragile — possibly paving the way for another General Election.
Minority government: Conservatives
Ignoring calls for her resignation, May said on Friday that she would seek to form a new government with a minority party. The prime minister will only be forced to resign if it becomes clear that she will not be able to obtain a majority through a coalition or loose alliances.
A hung Parliament — in which no single party has a majority — does not necessarily mean that a coalition would have to be formed. Instead, the next British prime minister could potentially also rely on a flexible arrangement in which one party sets up a “confidence and supply” deal with one or several smaller parties.
Under that kind of agreement, the smaller parties would not be part of the government but they would guarantee the prime minister their support on matters such as finances or confidence votes. In return, they would be able to hope for governmental concessions on some of their demands.
May’s minority government is likely to be supported by Northern Ireland’s right-of-center Democratic Unionist Party which won 10 seats. Together, both parties would have 328 seats in parliament. However, such an alliance would be fragile as May would need the support of nearly all MPs of her Conservative Party, many of whom are disgruntled by her loss of a majority on Thursday.
Other ad hoc alliances are also unlikely, as her political strategy in recent months has alienated many of the parties she would have to rely on for parliamentary votes. The Labour Party considers itself the main alternative to May’s conservative vision for Britain, whereas the Liberal Democrats would like to see Britain remain part of the E.U. The SNP remains frustrated by May’s earlier announcement not to grant Scotland another independence referendum anytime soon.
Minority coalition: Labour and Liberal Democrats
The last time the Liberal Democrats entered a coalition with a much bigger party in 2010, it did not end well for them. Being forced into major concessions by the Tories, the Liberal Democrats lost much support among many of their core voters and never quite recovered.
It is nevertheless possible that the Liberal Democrats could form a minority coalition with the Labour Party that would, for instance, aim at a softer exit from the European Union. The odds for such a coalition are low, though. The Liberal Democrats’ former leader, Ming Campbell, indicated an unwillingness to form such an alliance, telling the BBC on Thursday night, “We’ve had our fingers burned by coalition.”
Minority coalition: Labour and Scottish National Party (SNP)
Instead of forming an alliance with the coalition-skeptical Liberal Democrats, Labour could also join forces with the Scottish National Party to topple the Conservative Party.
Minority coalition: Labour and Scottish National Party and Liberal Democrats
Although it remains an unlikely scenario, it would probably be the preferred choice of many continental Europeans who still hope that Britain will make a U-turn in its decision to leave the E.U. Together, the Labour Party, the SNP and the Liberal Democrats would have 308 seats in Parliament — still fewer than May's Tories will have.
What unites members of all three parties is a certain degree of skepticism that the decision to leave the E.U. was the right one. However, as a minority coalition, the fragile coalition of three parties would still rely on the support of other, even smaller parties.
Minority government with a ‘confidence and supply’ deal: Labour and ‘supply’
Alternatively, the Labour party could try to go it alone by relying on a flexible “confidence and supply” deal with several smaller parties, such as the SNP.
Sturgeon suggested in March that she might be willing to agree to a “looser arrangement” with Labour under the framework of “confidence and-supply.”
Such an arrangement would be extremely fragile, however, as the government would have to unite policymakers from various sides of the political spectrum, including liberals and center-leftist Labour voters as well as Scottish independence supporters.