Rishi Sunak has warned there could be further bombing of Yemen if Houthi attacks on shipping continue, as he came under mounting pressure from MPs to clarify Britain’s long-term strategy for tackling the deepening crisis. The prime minister told parliament that a second round of RAF airstrikes, conducted on Monday night with the US, were taken in self-defence and rejected calls for MPs to be allowed a vote on whether to endorse the military action. The Houthis, who control the north and west of Yemen, said on Tuesday they would continue to fight on in support of Gaza, and told British and American aid workers to leave the part of the country they control within 30 days. Sunak said the UK and the US “are not seeking a confrontation” with the Houthis, but complained that the group had conducted at least 12 attacks on western shipping since the first round of British and American airstrikes on 12 January. That was sufficient to justify Monday night’s bombing raid, which saw RAF Typhoons strike two targets near Sana’a, the prime minister said, adding that the bombing of Yemen, one of the world’s poorest countries, may continue. “If necessary, the United Kingdom will not hesitate to respond again in self-defence,” said Sunak. “We cannot stand by and allow these attacks to go unchallenged. Inaction is also a choice,” he said, and went on to hint there could be additional efforts to halt the supply of weapons to the Houthis from Iran. “We must end the illegal flow of arms to the Houthi militia,” Sunak said, noting that the UK had “intercepted weapons shipments in the region before, including components of the very missiles used by the Houthis today”. Britain would work with “allies and partners” to try to disrupt and deter their supply in the future, he added. The foreign secretary, David Cameron, will visit the Middle East “in the coming days”, the prime minister said, as part of a fresh effort to ease tensions. Earlier this month the US and UK became engaged in bombing the Houthis in an attempt to halt a string of missile, drone and small-boat attacks mounted by the rebel group against international shipping in the southern Red Sea and Gulf of Aden, through which an estimated 15% of world seaborne trade passes. Experts believe the airstrikes, aimed at launch sites, radar facilities and underground bomb storage, could go on for several weeks because Houthi targets are dispersed and hard to hit, partly because the rebel group has endured nine years of civil war, including a bombing campaign led by Saudi Arabia. Sidharth Kaushal, a naval expert with the Royal United Services Institute thinktank, said: “We should expect a protracted crisis if the Houthis are not deterred from further action by the prospect of a protracted air campaign against them.” Houthi leaders remained defiant on Tuesday. The Houthi army spokesperson, Brig Gen Yahya Saree, said the allied attacks would not go unpunished or unanswered. Eighteen targets were struck overnight, the spokesperson added, but no casualty figures were given. British and American aid workers were also asked to leave Yemen within 30 days, according to a letter sent to aid agencies by the Houthi-controlled foreign affairs ministry. Aid workers already fear the series of airstrikes will dangerously weaken Yemen’s fragile humanitarian situation, in a country where imports of food and medicines have been in decline for several weeks. The Houthis say their attacks on shipping in the Red Sea, which began in mid October, are in support of Gaza. Propaganda put out by the group on social media juxtaposed pictures of Sana’a under attack with similar pictures in Gaza, or images of what appeared to be killed and wounded Palestinians. Jeremy Quin, a former defence minister and the new Conservative chair of the Commons defence committee, called on Sunak to acknowledge there might need to be “a prolonged, persistent, targeted campaign” in order to protect shipping in the Red Sea region. In reply, the prime minister sought at first to downplay the prospect. “I want to be absolutely clear that no decision has been taken to embark on a sustained campaign of the nature that he mentioned,” Sunak said, before emphasising: “We do reserve the right to take action in self-defence.” Labour and Scottish National party MPs all pressed Sunak to set out the UK’s strategy for resolving the Red Sea crisis, calling for diplomatic efforts and humanitarian relief in addition to military action. Keir Starmer, the Labour leader, said his party would judge further action against the Houthis on a case-by-case basis and that it backed the current “targeted action to reinforce maritime security in the Red Sea”. However, he also asked whether the military action would be effective, what efforts the UK was taking to build and enlarge support for a maritime coalition protecting merchant shipping, and what “concrete steps” were being taken “to help the people of Yemen who have suffered terribly as a result of that country’s civil war”. In reply, Sunak said an initial analysis showed “all intended targets were destroyed” and, in a later answer, added that there was “no evidence to suggest” there were civilian casualties caused by the latest round of bombing – or from the previous round of British strikes earlier in the month. Debbie Abrahams, a backbench Labour MP, said she shared concerns about “what the strategy is, what the contagion to the rest of the Middle East will be and that we are potentially bolstering the Houthis’ position in Yemen”. Ed Davey, the Liberal Democrat leader, called for MPs to be given a vote on military action against the Houthis, arguing that “the huge cross-party support for limited strikes” would “surely strengthen the signal he intends to give” to the Yemeni rebels. Sunak said MPs would be allowed a “general debate” in the Commons on Wednesday over the military intervention. But by convention such a debate is not followed by a vote. Recent parliamentary precedent has been to give MPs the right to approve military action, including the invasion of Iraq in 2003 and the bombing of Islamic State in Iraq and Syria in 2014 and 2015. However, formally the power is part of the royal prerogative reserved with the government, allowing for military action to be taken in self-defence without consulting parliament first. Summary legal advice released by the government sought to emphasise this point, and said that “dozens of serious attacks on shipping” by the Houthis had targeted “British flagged vessels, as well as the vessels of many other states”. The rebel group’s campaign had “culminated in an attack against HMS Diamond, involving multiple drones” in the Red Sea on 9 January, therefore justifying the UK in joining the US in attacking Yemen, using force to prevent further attacks.