Can you imagine the state this country would be in if it was intercepting ballistic missiles over Heathrow? Saudi Arabia has been accused in its part of the world of needlessly escalating a civil war it did not need to be involved in, but the Iranian-backed Houthis are beginning to show the world why the US and UK governments, if not media, have long considered this conflict essential to regional and international security. Saturday’s successfully swatted missile follows more than one hundred fired into more Southern areas of Saudi Arabia, and at the very least shows that it has real skin in the Yemen game. This is not an indulgent proxy war in a faraway land; it is a response to an existential threat on the border.

Thoughtful and considered analyses of the legitimacy of the war have been scarce. Rarer still have been constructive suggestions for how Britain could better contribute to shortening it, and minimise collateral damage. There have even been articles in newspapers here recently deploring Western intelligence sharing with the Saudis in Yemen, on the basis that our intelligence is sometimes used in strikes that lead to civilian casualties – entirely missing the irony that good intelligence is one of the best means of avoiding imprecise airstrikes.

War is inevitably a crude and cruel means of resolving international differences. It deserves to be intensely scrutinised, so that civilian casualties are minimised. However, the horror of such incidents should not in isolation be sufficient to de-legitimise the entire operation.

There has been far too little argument in this country about why there should be a campaign in Yemen. Al Qaeda currently occupies huge swathes of Yemeni land, from which it is able to plan international terrorist operations. The United States announced last month that it was imposing sanctions on its leadership in Yemen, but that is hardly going to force them to walk. It is also difficult to see how Britain could benefit from a Houthi-led regime in the country. We should be concerned that pressure on the UK government to remove itself from the picture will only mean in practice that the Saudi-led coalition continues to fight a war that needs to be won; but without British intelligence, humanitarian assistance, and strategic support.

Before the Houthis drove the government out of Sana’a, the country was a close ally of Saudi Arabia, with whom it shares a land border as well as a profound cultural heritage as part of the Arabian peninsula. The Houthi Revolutionary Committee is an Iranian proxy. The coup against President Hadi represented an attempt by an expansionist rival to extend its reach into the ‘soft-underbelly’ of the two leading Gulf states. It is inconceivable that Riyadh could have allowed Iran to succeed. If such events were happening on our doorstep, we would not have hesitated to act.

One of the world’s most lethal terrorist groups now controls territory the size of a small country in central Yemen, directing operations out of the safe zone it has established. Much of the Gulf coalition’s focus, for which the Americans understandably provide support, is on driving Al Qaeda from this dangerous position in the Arabian peninsula. It would therefore be entirely irresponsible to pressure the Saudi-led coalition to withdraw, unless there is a plan to replace them with Western forces.  I do not see much prospect of that happening.

There is also a direct security interest in our preventing Iran from installing a proxy government in Yemen. Firstly, the Gulf States are much better allies of ours than Iran, which has an entrenched distrust of Britain and a hatred of America. Iranian political discourse is full of accusations about BBC and MI6 influence in the country. It does not make sense to jeopardise good relationships with friendly countries for one that at best actively dislikes all that we stand for – and at worst is sponsoring efforts to destroy our way of life.

Secondly, allowing the Houthis to prevail could conceivably, if not probably, lead to a devastating war between Iran and Saudi Arabia. Houthi rebels will continue to fire rockets into Saudi territory, without any restraint from their masters. It does not require much pessimism to imagine that they would carry on doing so after any temporary truce is agreed. Iran is probably comfortable with the idea of Saudi Arabia continuing its fight in Yemen; they are spending billions every month and drawing international condemnation. But there would appear to be no incentive for Tehran to give peace a chance.

Historically, Britain built its admired and valuable reputation by taking leadership positions on international issues. It would be both right and advantageous for us to rediscover that authority by setting out clearly why we are backing the Gulf coalition to succeed. Scrutinising the conduct of the war is only one of four roles we need to play in this conflict. Britain must also provide military and intelligence support to our allies, humanitarian assistance to the Red Crescent, and pressure on the Iranians to withdraw their sponsorship of the revolutionaries. If the latter sounds unrealistic, bear in mind that President Trump has just put the 2015 nuclear deal with Iran back on the table. There may then actually be a unique opportunity to negotiate on Yemen.

Geoff Hoon was UK Defence Secretary between 1999 and 2005