The latest strikes against Houthi rebels send the "clearest possible message" that they must stop attacking ships in the Red Sea, Lord Cameron has said.
Last night, the US and UK carried out joint attacks on Houthi military targets in Yemen for the second time.
The strikes targeted a Houthi underground storage site and locations associated with the Houthis' missile and air surveillance capabilities, a joint statement from the UK, US, Bahrain, Australia, Canada and the Netherlands said.
The foreign secretary said the UK has "no quarrel" with the Yemeni people, but Britain and the US want to show that "we back our words and our warnings with action".
Speaking to broadcasters on Tuesday he said: "Since we last took action 10 days ago, there have been over 12 attacks on shipping by the Houthis in the Red Sea.
"These attacks are illegal, they are unacceptable.
"What we have done again is send the clearest possible message that we will continue to degrade their ability to carry out these attacks while sending the clearest possible message that we back our words and our warnings with action."
Lord Cameron said "we shouldn't accept the Houthi narrative" that the strikes in the Red Sea are connected to the conflict in Israel and Gaza, saying the Yemeni government doesn't accept that either.
"What the Houthis are doing is attacking shipping indiscriminately and trying to close a vital sea lane, whereas we want to keep that sea lane open."
The Ministry of Defence said four RAF Typhoons, supported by a pair of Voyager tankers, "joined US forces in a deliberate strike against Houthi sites in Yemen".
It added that Paveway IV precision-guided bombs were used to strike "multiple targets at two military sites in the vicinity of Sanaa airfield".
The MoD continued: "These locations were being used to enable the continued intolerable attacks against international shipping in the Red Sea."
It said a "very rigorous analysis" was used to minimise any risk of civilian casualties, which included the decision to attack at night.
The Houthis support Hamas and have been attacking ships they claim are either linked to Israel or heading to Israeli ports. However, several of the group's attacks have been on vessels from other countries.
Houthi media said the Yemeni capital, Sanaa, was among the targets, along with several other areas.
Jamal Hassan, who lives in south Sanaa, said two strikes landed near his home, setting off car alarms in the street.
Aircraft were heard flying over Sanaa, an Associated Press journalist said.
Rishi Sunak, the prime minister, and US President Joe Biden spoke on the phone on Monday about ongoing attacks against naval and merchant vessels, the White House said.
They also discussed trying to secure the release of hostages still being held by Hamas in Gaza, the US added.
Grant Shapps, the defence secretary, said the latest attacks would "deal another blow" to the Houthis' "limited stockpiles and ability to threaten global trade".
The group had defied a warning to stop.
After the first attacks involving British forces, the UK's Ministry of Defence said "particular care was taken to minimise any risks to civilians" and "any such risks were mitigated further by the decision to conduct the strikes during the night".
The latest attacks were also carried out under the cover of darkness.
Yemeni press agency, SABA, reported earlier this month that the first UK/US attacks took place in the capital, Sanaa, and the governorates of Sadah, Hodeidah, Taiz, and Dhamar.
A Houthi official said the initial attacks killed at least five people and wounded six, adding that they would not go "unanswered".
The US subsequently launched another strike against a Houthi target in Yemen.