Union of Britain and France (aka "Britance")
Formed, of course, by Guy Mollet's proposal during the Suez Crisis for a Franco-British political union being adopted.
New Democratic Party / Nouveau Parti démocratique: The main centre-right party, formed by a merger of the Conservative and Unionist Party of the United Kingdom and the Popular Republican Movement of France, with some additional smaller 'divers droite' French parties added in as well. Half the National Centre of Independents and Peasants also joined, that party fracturing down the middle. Considered to have its centre of power in Britain due to the Conservatives being more organised and in power at the time the merger happened, whereas the French Right was scattered and chaotic. The name was chosen by Harold Macmillan, taking the opportunity to rebrand with a more forward-looking label.
Labour Party / Parti travailliste: The main centre-left party, formed by a merger of the Labour Party (and Labour Co-operative Party) of the United Kingdom and the French Section of the Workers' International. It has an affiliation agreement with the portion of the Irish Labour Party that stands candidates in Northern Ireland. Its centre of power is roughly balanced between the two countries.
Radical Liberal Party / Parti Radical Libéral: Classical liberals. Formed by a merger of the Liberal Party of the United Kingdom, the Radical Party of France and the more left-wing half of the National Centre of Independents and Peasants, the other half going to the New Democrats. Its centre of power is considered to be in France.
Communist Party of Western Europe / Parti communiste de l'Europe Occidentale: Communists, mostly of the take-orders-from-Moscow stripe but with some internal disagreements. Formed by the merger of the Communist Party of Great Britain and the French Communist Party. Initially opposed the union and refused to acknowledge it, but had to change this to comply with new election laws and changed its name in turn. Its centre of power is undoubtedly in France.
Alliance for Celtic Liberty / Alliance pour la liberté celtique: Due to new election laws requiring registered parties (i.e. those liable for funding, party political broadcasts, etc.) to stand candidates in all constituent parts of the Union, the Scottish National Party, Plaid Cymru and moderate Irish republicans created an electoral alliance that also incorporated more minor Cornish and Breton groups in order to fulfil the new rules. Although the formation of the group was for purely pragmatic reasons, it has led to more Celtic internationalism.
United National Party / Parti nationale uni: Currently minor alliance of far-right groups, their main cause being opposition to immigration and defence of colonialism (pied-noirs, Rhodesia, etc.)
Anti-Union Group / Bloc contre-union: A loose alliance of groups opposed to the Franco-British Union, which have been forced to work together by the new election rules despite the fact that they mostly hate each other.