Pro-EU supporters outside the British Parliament buildings in London on Dec. 12, 2018. Mike Newberg | CNBC

Opposition lawmakers have overwhelmingly welcomed the U.K. Supreme Court's ruling that Prime Minister Boris Johnson acted unlawfully by suspending parliament for five weeks. However, they remain divided over the best approach to Brexit ahead of the Parliament's reopening late Wednesday morning. The British premier, flying back overnight from the UN General Assembly, appeared far from worried by the court defeat in a joint press conference with President Trump late Tuesday in New York, ignoring questions about a possible resignation and indeed hinting that a further suspension of the parliament was still possible. The Parliament is set to reopen Wednesday with Johnson presiding over a minority government, and buoyant opposition lawmakers arrayed against him.

Who's saying what?

Labour leader Jeremy Corbyn insisted he wants Johnson out of office, and this week he and his allies encouraged party members to endorse a policy at its annual conference that calls for Labour to maintain a broadly neutral stance on the U.K.'s continued EU membership. Twice this month Corbyn has shied away from the pursuit of a fresh national election, and on Tuesday he suggested that if Labour were to win an election, it would only hold a referendum six months later. Several other senior legislators have said they cannot agree on the best approach to break the parliamentary deadlock that has dogged British policy on Brexit for almost a year now.

Veteran Labour lawmaker and former minister Ben Bradshaw told CNBC this week his party wanted to ensure that "the people's voice in this country is heard either through another general election or preferably another referendum." Meanwhile, the Westminster leader of the Scottish National Party - Labour's chief rival in Scotland - was typically blunt about his group's preferred course of action. "The opposition has to come together," said Ian Blackford, "force a vote of no-confidence, take Boris Johnson out of office and have a general election, that is the way that we should be going." The Brexit spokesperson for the Liberal Democrats, Tom Brake, insisted his party would first work to strengthen that existing legislation that prevents an October Brexit. "There are certain things that we can do," said Brake, "to be absolutely certain that the prime minister will be required to seek an extension." John Bercow, the Speaker of the House of Commons (the lower chamber), who called for parliament to reassemble just minutes after the Supreme Court's ruling, has said he will offer parliamentarians free rein starting Tuesday, meaning that opposition legislators can ask questions of government ministers or even take control of the parliamentary agenda.