The SuezCanal and Red Sea are vital lifelines for Western Europe and certainly the Brits and French have the means to wreak havoc on the Houthis and open the Suez Canal. Why have they not taken charge?
Blockade Yemen, take out their offshore oil production which is most of their production and take out their refining capacity, the blockade would starve them out. Yemen is only about 20% self sufficient in food. They will cooperate or starve in the dark.