the UK if it had an electoral system similar to Japan, and still had Ireland.
The parties in Ireland are:
Center: the spiritual successor to the Irish Parliamentary Party. As its name suggests, it is smack-dab in the center. Everything they do is for winning votes. They are responsible for Westminster governments giving huge amounts of largesse to Ireland over the decades, propping up both Labour and Conservative governments over the years. It is vaguely autonomist, and includes within its ranks both hardline unionists and hardline separatists/nationalists.
Unionist: compared to Center, it is more right-wing, classical liberal, and pro-business (aka Ireland Tories). Its Dublin Region seats vote for it fairly reliably but are still rather marginal, and are vulnerable to tactical voting from other parties. The Unionist party, as its name suggests, is most distinguished by its rock-solid unionism.
Irish Labour: the main left-wing political force on the unionist side. It has been on the decline in recent years due to scandals, and relative inability to win young voters.
Democratic Unionist Party: the voice of hardline Protestants in Ulster who still feel unhappy about Home Rule including Ulster within the Irish Parliament. They only stand in Ulster-based constituencies. They are allies of the Unionists, "loyalists", who represent an even more hardline unionist constituency. They frequently move in concert with the Unionists to lock out Sinn Fein.
Sinn Fein: the nationalist/separatist party, the only notable party supportive of Irish independence. Their advocacy resulted in a referendum being called on the question in 2014, but the result was 65%-35%, a landslide for the status quo wider than polls suggested. It has won over left-leaning young voters due to Labour being seen as stale. Nonetheless they regularly pile up wasted votes that do not translate into seats, due to Unionist maneuvering. The clear majority of their votes come from Ulster, though they've became the main left force in portions of rural Ireland.
Alliance: a liberal party aligned with the Liberal Democrats. They only stand in Ulster-based seats. They take no position whatsoever on the unionist vs nationalist/separatist debate, and advocate equitable and fair treatment for all. They regularly win PR block seats, but rarely win any constituency seats.
The 2017 GE was called by Conservative PM Theresa May because "Britain needed certainty, stability and strong leadership following the EU referendum*". Going into the election, the Conservatives had a minority government with confidence and supply from the Unionist party. She hoped to win a majority. But instead, after a bad campaign, the Tories backslided in seat count, while still remaining ahead of Labour. In the end, she was able to muster a Commons majority by getting unconditional support from the Unionists (again) and conditional support from Center. This was enough for 243 seats, just enough for a majority. Press speculation has since been rife of Center potentially pulling its support for May's government, but in reality, the island is getting huge sums of money from Westminster, and the withdrawal agreement negotiations have shown a very clear Center influence. Many people on the island of Great Britain perceive May to be allowing Center to control her government.
*=Brexit referendum goes 53.2-46.8% ITTL due to Ireland voting more solidly in favor of Brexit than England and Wales. Center, Irish Labour, and the DUP were supportive of Brexit; and the Sinn Fein, Unionist, and Alliance parties were opposed.