"We've demonstrated that we're prepared to follow words and warnings with action and that is incredibly important," Cameron told broadcaster Sky News.
He suggested further strikes could occur if the Huthi rebels, who control much of Yemen, continue to target ships in the Red Sea.
"We have to act. Not acting is also a policy and it was a policy that wasn't working," he said.
"It's not just the goods that are coming to this country... it is also grain ships on their way to Ethiopia and Sudan to feed some of the poorest and hungriest people in the world."
He accused Iran, which backs the Huthis, of being a "malign actor in the region".
Some MPs complained that they were unable to debate Thursday's air strikes before they occurred.
Cameron said there would be a statement in parliament on Monday when both houses could raise questions.
Opposition leader Keir Starmer, widely tipped to become prime minister later this year, told the BBC he would back further action "on its merits", although the decision ultimately rests with the government.
Cameron's comments echo those of US President Joe Biden, who said he would "not hesitate to direct further measures to protect our people and the free flow of international commerce as necessary".
Around 12 percent of global trade normally passes through the Red Sea.
But since mid-November, the attacks have prompted many shipping firms to take the longer route around the tip of Africa, disrupting supply chains and putting upward pressure on inflation.
The Huthis say they are acting in solidarity with the Palestinians of Gaza, where the Hamas-run health ministry says nearly 24,000 people, mostly women and children, have been killed by Israeli forces in the past 100 days.
Israel began its relentless bombardment and ground offensive in Gaza after Hamas staged attacks in Israel on October 7, although Cameron said the UK government saw the two issues as "completely separate".
He took aim at Tehran, saying there was "no doubt that the malign actor in the region who is behind these proxy groups is Iran".
"Iran backs Hamas. They back Hezbollah. They back the Huthis. They provide them with weapons," he told Sky News.
"We know what they're doing. We know what they're doing is wrong. We call them out for it," he added.
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