My summary of the statements from Russia/US/UK/China about the legality of US and UK's attacks on Yemeni territory

Russia:

VASSILY A. NEBENZIA (Russian Federation) noted the massive strike on Yemeni territory on 11 January by “a so-called international coalition”, headed by the United States and United Kingdom and including Australia, Canada, Bahrain and the Netherlands ...

... The exercise of the right to self-defence does not apply to commercial shipping, he said, noting that freedom of navigation is governed by the United Nations Convention on the Law of the Sea, which provides for negotiation and arbitration in the event of violations.

... the concept of piracy does not apply in this case and pointed out: “Even if we’re talking about pirates, the Convention gives you the right to seize a pirate vessel and prosecute the crew and not to bomb yet another country back to the Stone Age.”

... resolution 2722 (2024) does not authorize the arbitrary acts that the United States and its satellites are carrying out in Yemen.

UK:

BARBARA WOODWARD (United Kingdom) recalled that on 9 January, the Houthis attacked naval vessels of her country and the United States. On 11 January, her country took limited, necessary and proportionate action in self-defence alongside the United States, with the non-operational support of the Netherlands, Canada, Bahrain and Australia.

... The United Kingdom published a summary of its legal position on its strikes against the Houthis and reported to the Council in writing in accordance with Article 51 of the Charter of the United Nations.

US:

LINDA THOMAS-GREENFIELD (United States) noted that in response to ongoing and escalating Houthi attacks in the Red Sea, the United States and United Kingdom, with support from four countries, conducted a number of joint strikes on Houthi targets in Yemen to disrupt and degrade their ability to continue those reckless attacks. The strikes were necessary and proportionate, consistent with international law and the United States’ inherent right to self-defence under Article 51 of the Charter of the United Nations. ...

She noted that on 18 December, the United States formed Operation Prosperity Guardian, a 22-country defensive coalition, citing ongoing Houthi attacks and her country’s military response, while pursuing a diplomatic response. She cited resolution 2722 (2024), which references the inherent right of Member States to defend their vessels. ...

China:

ZHANG JUN (China) expressed grave concern over the launch of strikes against the Houthis by the United Kingdom and the United States. His country called repeatedly on the Houthis to immediately cease their attacks and harassments on commercial vessels and respect the navigation rights of the commercial vessels of all countries. ...

... Expressing regret over the latest military actions against Yemen, he observed that they destructed infrastructure and caused civilian casualties. They also heightened security risks in the Red Sea and risked undermining the ongoing political process. The Council has never authorized any State to use force. Their military actions are at odds with Council resolution 2722 (2024). No country shall misinterpret or abuse international law. ...

Russia:

Mr. NEBENZIA (Russian Federation), taking the floor a second time, called the arguments put forward by the United States and the United Kingdom “very weak”. There is no legal basis on which to justify their attacks on sovereign Yemen, he underscored, questioning what right to self-defence can exist when London and Washington, D.C., are thousands of miles away from the Gulf of Aden. Disproportionately and illegally bombing another State is not the same as defending commercial shipping. “The Anglo-Saxon juror and their satellites”, he said, are once again flagrantly violating the Charter of the United Nations and other norms of international law, further destabilizing the situation in a Middle East already in flames. ...

US:

Ms. THOMAS-GREENFIELD (United States) said that her delegation was clear in its statement — “despite the fact that my Russian colleague thinks it was weak”. The United States carried out action under Article 51 of the Charter of the United Nations to ensure freedom of navigation and the free flow of commerce. ...

UK:

Ms. WOODWARD (United Kingdom) said that her delegation has both “published a summary of our legal position on last night’s strikes” and reported to the Council in writing in accordance with Article 51 of the Charter of the United Nations.

What is this Article 51? https://www.un.org/en/about-us/un-charter/full-text

Article 51

Nothing in the present Charter shall impair the inherent right of individual or collective self-defence if an armed attack occurs against a Member of the United Nations, until the Security Council has taken measures necessary to maintain international peace and security. Measures taken by Members in the exercise of this right of self-defence shall be immediately reported to the Security Council and shall not in any way affect the authority and responsibility of the Security Council under the present Charter to take at any time such action as it deems necessary in order to maintain or restore international peace and security.