On 29 January the House of Commons voted in favour of the "Brady amendment", which indicates that there would be a Parliamentary majority in favour of the Withdrawal Agreement and Political Declaration (WA) if the legal text were amended to replace the backstop arrangement set out in the Northern Ireland protocol with "alternative arrangements". During the House of Commons debate, Brexit Secretary Stephen Barclay repeatedly refused to spell out what those arrangements might be, prompting one opposition MP to observe that the only available information was that they would be "alternative", and that they would be "arrangements". Within minutes of the vote, President of the European Council, Donald Tusk, reaffirmed the EU position, which is that the WA is not open for renegotiation.

The House of Commons also approved the "Spelman-Dromey" amendment, which asks (but cannot oblige) the government to rule out a "no deal" Brexit.

Taken together, the amendments approved by the House of Commons do not remove, or even materially reduce, the risk of a "no deal" Brexit on 29 March 2019. To avoid that outcome, Parliament would have to enact primary legislation to repeal or override key elements of the EU (Withdrawal) Act 2018 and also other key provisions, such as section 31(5) of the Taxation (Cross Border Trade) Act 2018, which prevents the UK government from entering into any form of customs union with the EU unless specifically authorised by an Act of Parliament. Consequently, unless and until the details of any "alternative arrangements" are set out, there can be no guarantee that the majority gathered by the Brady amendment would translate into a sufficiently durable majority to unpick the legislation that leads inexorably to a "no deal" outcome.

From an international perspective, Brexit is being watched with a mix of fascination and concern. As the House of Commons was creating what Guardian columnist John Crace has taken to calling "Schrodinger's Brexit", members of the Irish-American caucus in the US Congress tabled a resolution opposing the re-imposition of a hard border in Ireland. Tabling the resolution, Congressman Brendan Boyle argued that "a hard border would eliminate the free flow of people between Northern Ireland and the Republic of Ireland, which has proved fundamental to promoting peace and unity". Those concerns are also shared by Congressman Richard Neal – a direct participant in the process that led to the Good Friday Agreement, and now head of the Ways and Means Committee in Congress that would play a key role in overseeing any future free trade agreement between the UK and the US. Consequently, concerns of the sort expressed on Capitol Hill go directly to a key element in the UK's post-Brexit agenda, which depends on the negotiation of trade agreements. That, in turn, depends on international perceptions of the UK as a reliable partner.

The UK government can point to the current text of the WA. Article 1 of the Northern Ireland protocol states that it is "without prejudice to the provisions of the 1998 Agreement regarding the constitutional status of Northern Ireland and the principle of consent, which provides that any change in that status can only be made with the consent of a majority of its people", and to paragraph 3 of that Article, which emphasises that the protocol "sets out arrangements necessary to address the unique circumstances on the island of Ireland, maintain the necessary conditions for continued North-South cooperation, avoid a hard border and protect the 1998 Agreement in all its dimensions ". However, the UK government's understanding and commitment to those principles has, at several points during the Brexit process, been open to question. For example, images of the UK Prime Minister giving a speech from behind a lectern emblazoned with the words "Global Britain" sit uneasily with the Prime Minister's references to "our precious Union", which refers to the United Kingdom of Great Britain and Northern Ireland.

Perceptions matter. Achieving an "orderly Brexit" is not just a question of avoiding traffic jams on the road to Dover. Brexit requires the UK to extract itself from a complex and deeply-integrated set of international agreements and treaty obligations. Concerns that the UK might walk away from obligations have a direct bearing on the tone and credibility of negotiations intended to avoid a "hard" Brexit, and on any subsequent negotiations that the UK might seek with other key trading partners. Speaking in Brussels on 23 January 2019, Michel Barnier said: "Without ratification there will be no Withdrawal Agreement and no transition agreement; nor will there be the mutual trust we need in order to build our future relationship".