Jeremy Hunt has called the US’s escalating confrontation with Iran over the assassination of Tehran’s top general an “incredibly dangerous game of chicken”.

He made his comments as the Foreign Office updated its travel advice on Saturday, warning British nationals against going to Iraq apart from essential travel to the Kurdistan region in the north of the country. The government is also urging Britons to avoid all but essential travel to Iran.

It has also updated its travel advice for Lebanon and urged British nationals in the country to remain vigilant and issued similar travel advice for British nationals in Israel, Afghanistan and Palestine.

As concerns grow about reprisals over the killing of Qassem Suleimani in a US drone strike in Baghdad, the former foreign secretary urged the UK to use its position as a key US ally to push Donald Trump to take a more consistent foreign policy approach.

US failing to give UK warning of military strikes, says senior MP Read more

Suleimani, who spearheaded Tehran’s military operations in Iraq and Syria as commander of the elite Quds force, was considered the second most powerful figure in Iran. The 62-year-old, who was implicated in tens of thousands of civilian deaths, was killed on Friday morning when his vehicle was targeted by a drone as local allies from the Popular Mobilisation Forces drove him from the airport.

Hunt, who served as foreign secretary before standing down in July after losing the Tory leadership race to Boris Johnson, told BBC Radio 4’s Today programme: “It’s an incredibly dangerous game of chicken going on at the moment because both sides have calculated that the other side cannot afford and doesn’t want to go to war.

“So they are doing increasingly extreme things, not just the assassination of general Suleimani, but the bombing of the Saudi oil facility last September is another example of this. And, of course, it is true that neither side wants to go to war but it’s also true that both sides are compelled to react when things like this happen and that is the risk in the current situation.”

Play Video 1:37 Aftermath of US airstrike that killed top Iranian general Qassem Suleimani – video report

Hunt said it was impossible to predict whether the reaction to the killing would be immediate or play out longer term. “It’s clear that they [Iran] will have to react and that will have been calculated by the United States,” he said. “This is a very difficult situation for allies of the United States, like ourselves, because I happen to be someone who believes the world is safer when America is involved in what’s happening beyond its shores.

“The UK cannot afford to be neutral if we want to be a serious global player but this is a very, very risky situation and I think that the job we have to do is as one of the US’s closest allies is to use our influence to argue for more consistent US policy. Because sometimes the US seems torn between a desire to appear strong and decisive and influential across every region in the world and the other desire, which is to get its troops home, to reduce the risk to American lives on the ground and to concentrate on the big power competition with China.

“And it’s those two conflicting forces that are tugging at the president and that makes people miscalculate because I’m sure, Suleimani thought that the US might not react to some of the things he had been plotting and planning and that was, of course, a big miscalculation. And it’s those miscalculations that are dangerous.”

Asked whether he believed Trump miscalculated by ordering the strike, Hunt said: “Only time will tell. But, as I say, I would rather an America that was active and involved in the region. Despite being known for his rhetoric, actually what has characterised Trump is his caution in deploying troops.”

Hunt said the apparent decision by the US not to inform the UK in advance of the strike was not in the spirit of its relationship as a close ally. He said: “Well, I think it’s regrettable because, as one of the US’s closest allies, I think it’s an important aspect of that relationship that there are no surprises in the relationship.

“But it may also have been because they didn’t want to put us in a difficult position of asking us to make a judgment whether we agreed or not with what was done. I think our relationship with the US is one where we shouldn’t overestimate our influence, but we shouldn’t underestimate it either.”

Jeremy Corbyn has written to the prime minister, who has been on holiday on the private Caribbean island of Mustique, calling for an urgent meeting of the privy council to discuss whether the strike had heightened the risk of a terrorist attack in the UK.

In his letter, the Labour leader asked if the UK had spoken to the UN to discuss consequences for peace and security and what measures had been taken to ensure the safety of UK nationals.