But how far have they thought it through? The operations risk a lot, will almost certainly not achieve their goals and are already strengthening the enemy.
The Houthis and their Iranian patrons laid a trap and Britain and America have arguably walked, or flown right into it.
The allied aim is to neutralise the threat posed by the Houthi rebel forces against international shipping in the Red Sea, through which a huge amount of oil and goods pass.
Once a rag-tag rebel army, the Houthis are now a fighting force to be reckoned with, dominating much of Yemen and armed and trained by Iran.
They have been attacking ships since the start of Israel’s Gaza offensive in solidarity with their Arab brothers, they say.
The Houthis are hitting the West where it hurts – but to be successful, the British-American airstrikes must entirely neutralise their threat to the Red Sea.
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1:42
Transport minister Huw Merriman says ‘we are not ruling out further strikes against the Houthis’.
While any threat persists, international shipping must avoid the Red Sea because of the punitive cost of insurance which has in some cases risen 20-fold.
That degree of success is unfeasible. Ask the Saudis who failed to deter the Houthis despite eight years of military action supported by Gulf allies, the UK and the US.
But more to the point, the capability the Houthis are using to threaten shipping is mobile and easily hidden in the desert wastes of Yemen.
The airstrikes will certainly degrade the Houthis.
‘Plucky’ Houthis revelling in popularity
But they only need to continue threatening shipping. For that, the Houthis need to hang on to a handful of portable assets and render the Red Sea unviable as a conduit for international shipping.
And despite everything British and American jets threw at them two weeks ago, they’ve managed to keep up the threat, letting loose missiles at shipping regardless.
Meanwhile the Houthis are benefiting from the military action where it counts for them in the arena of Arab public opinion.
While corrupt, decadent autocratic Arab regimes, as millions of Arabs see them, are doing nothing about Gaza, the plucky Houthis are. And they are revelling in it.
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2:35
Meet ‘Timhouthi Chalamet’
As Sky News has shown today, the conflict is making celebrities of the Houthis, like the man they are calling Timhouthi Chalamet, a young photogenic Houthi online influencer.
And the Houthis have successfully drawn Britain and America deeper into the Middle Eastern conflict that’s swirling around Gaza.
Rishi Sunak may claim the airstrikes are “unrelated” to Gaza but that’s frankly nonsense. The Houthis have made this explicitly about Gaza. They began their action over the war there and will end it, most analysts agree, once there is a ceasefire.
The British and Americans are letting loose armaments worth tens of millions on one of the world’s poorest countries to allow Israel to do the same in another equally impoverished area.
That is certainly how this is being seen by hundreds of millions.
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None of that is any good for either countries’ standing in the Arab world and beyond. It is a PR disaster for Britain and America and a huge boost for the Houthis and by association their Iranian patrons.
The airstrikes may be blowing up bunkers and weapons stockpiles or rearranging sand in the desert but in the battle for hearts and minds across the Middle East, they are handing a victory to Iran and its allies.
And they are almost certainly not going to make the Red Sea a viable international trade route again, not until Israel ends its offensive in Gaza.
South Korea’s parliament has voted to impeach acting President Han Duck-soo.
The move could deepen a constitutional crisis triggered by a short-lived period of martial law declared by Mr Han’s predecessor, Yoon Suk Yeol.
After the vote on Friday, Mr Han said he will step aside to avoid more chaos.
The opposition brought impeachment proceedings against him over his refusal to immediately fill three places on South Korea’s Constitutional Court – where the former president is on trial.
Three justices had been approved by parliament – where the opposition Democratic Party has a majority – but Mr Han said he would not formally appoint them without bipartisan agreement.
South Korea’s constitution says that six justices on the nine-member Constitutional Court must agree to remove an impeached president, meaning the current justices must vote unanimously to remove Mr Yoon.
The court has said it can deliberate without the full nine-member bench.
Leader of the opposition Lee Jae-myung had vowed to go ahead with the impeachment, accusing Mr Han of “acting for insurrection”.
Now that Mr Han – who is also prime minister – has been impeached, his finance minister Choi Sang-mok is set to take over as acting president.
Politicians in the 300 parliament voted 192-0 to impeach him. Governing party politicians boycotted the vote.
Following the vote, Mr Han said he would respect the decision and will await a ruling from the Constitutional Court on the impeachment motion.
Mr Han will be stripped of the powers and duties of the president until the Constitutional Court decides whether to dismiss or reinstate him – the same as with Mr Yoon.
Russian President Vladimir Putin has said he would be open to peace talks with Ukraine in Slovakia “if it comes to that”.
Mr Putin said Slovakian Prime Minister Robert Fico, who this week visited the Kremlin, had offered his country as a location for negotiations as the war in Ukraine nears the three-year mark.
The Russian president said the Slovakian authorities “would be happy to provide their own country as a platform for negotiations”.
“We are not opposed, if it comes to that. Why not? Since Slovakia takes such a neutral position,” Mr Putin said, adding he was resolved to end the conflict in Ukraine, which started with a land, air and sea invasion of Russia’s smaller neighbour in February 2022.
Ukraine is yet to comment on Slovakia’s offer but President Volodymyr Zelenskyy has repeatedly criticised the country, which borders Ukraine, for the friendly tone Mr Fico has struck towards Russia since his return to power after an election in 2023.
Mr Fico has been critical of EU support for Ukraine, where millions have been displaced since Mr Putin’s decision to launch a “special military operation” to “denazify” and “demilitarise” the 37 million-strong country.
More on Russia
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0:52
Mr Zelenskyy on North Korea and Slovakian PM in Moscow
Mr Putin has repeatedly said Russia is open to talks to end the conflict with Kyiv, but that it would nevertheless achieve its goals in Ukraine.
He has previously demanded Ukrainewithdraw its bid to join NATO and asked it to recognise Russia’s gains. Both Kyiv and the West have rejected those demands.
But while Mr Zelenskyy had for most of the conflict insisted Ukraine would keep fighting until it regained control of its territories, his position on negotiations now appears to have shifted.
Inan interview with Sky News, Mr Zelenskyy suggested a ceasefire deal could be struck if the Ukrainian territory he controls could be taken “under the NATO umbrella”.
This would then allow him to negotiate the return of the rest later “in a diplomatic way”.
The Ukrainian leader admitted last weekhis forces would be unable to recapture any territories occupied by Russia in the east of Ukraine and the Crimean peninsula.
While Kyiv would never recognise Russia’s rule, he said diplomacy is the only option to get Mr Putin to withdraw his army.
The war in Ukraine has taken a devastating toll on Russia too. UK government and military analysis estimates that Russia has lost around half a million troops killed or wounded in Ukraine.
Such is the pressure on manpower that The Kremlin turned to one of its remaining allies, North Korea, to provide additional forces.
It’s thought 10,000 to 12,000 troops were sent in October to fight alongside the Russian military in the fighting in the Kursk region.
However it’s suggested their lack of combat experience has resulted in heavy losses, with Mr Zelenskyy saying earlier this week that 3,000 North Korean troops have already been killed and wounded.
Donald Trump has suggested the US could take control of Canada, Greenland and the Panama Canal in a series of Christmas Day social media posts.
The president-elect wished a merry Christmas to all on his Truth Social platform, “including to the wonderful soldiers of China, who are lovingly, but illegally, operating the Panama Canal”.
In the lengthy posts, Mr Trump referred to the American lives lost during the canal’s construction and said the US “puts in billions of dollars in ‘repair’ money, but will have absolutely nothing to say about ‘anything’.”
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1:50
Panama Canal, strange sounds and Elon Musk
He also mocked Canadian Prime Minister Justin Trudeau as “governor” and again suggested the country could be turned into a US state – following similar comments made in recent weeks.
“If Canada was to become our 51st state, their taxes would be cut by more than 60%, their businesses would immediately double in size, and they would be militarily protected like no other country anywhere in the world,” he wrote.
In another post, Mr Trump, 78, said he had encouraged former ice hockey star Wayne Gretzky to run for prime minister but he “had no interest”.
He also addressed “the people of Greenland, which is needed by the United States for national security purposes and, who want the US to be there, and we will!”
It comes after Mr Trump renewed the call he made during his first term in office for the US to buy Greenland from Denmark.
The world’s largest island, which sits between the Atlantic and Arctic oceans, is 80% covered by an ice sheet and is home to a large US military base. Greenland gained autonomy from Denmark in 1979.
The island’s Prime Minister Mute Egede has insisted Greenland is not for sale.
Mr Trump has also previously threatened to retake control of the Panama Canal, accusing Panama of charging excessive rates to use the crucial trade passage and warning of potential Chinese influence.
Panama’s President Jose Raul Mulino previously said his country’s independence was non-negotiable and that China had no influence on the canal’s administration.
The canal is a critical waterway for world trade, connecting the Atlantic and Pacific oceans and allows ships to avoid lengthy and hazardous journeys around the southernmost tip of South America by cutting through the middle of the Americas.
After the ambitious project was opened in 1914, the canal and surrounding territory were controlled by the US until an agreement with Panama in 1977 paved the way for it to return to full Panamanian control in 1999.
China does not control the canal but a subsidiary of Hong Kong-based CK Hutchison Holdings has long managed two ports at the canal’s Caribbean and Pacific entrances.