Yemen’s Ansarullah movement, better known as the Houthis, has launched drone and missile attacks on vessels in the Gulf of Aden and Red Sea since November, demonstrating its ability to disrupt the global economy in response to the Gaza war.  British and US forces have retaliated by bombing Houthi targets for almost a month.

The ultimate outcome of the aerial campaign, which London and Washington insist is not a war, remains to be seen. But Britain and the US are likely set for a prolonged struggle against Ansarullah near the Bab Al-Mandab Strait—unless and until Israel agrees to a ceasefire in...