Leaders of the five main Westminster opposition parties have united to call on the two Conservative leadership candidates to agree to hold a full parliamentary or public inquiry into how ministers continued to provide assurances to MPs that arms sales to Saudi Arabia were lawful when no such robust internal check had been made.

The letter is a sign of how much UK foreign policy, especially towards the Middle East, might change if the Conservatives lose power, and how much inter-party consensus there is between the opposition parties on foreign policy, if not on Brexit.

The letter, organised by the Scottish National party Westminster leader, Ian Blackford, has been signed by Jeremy Corbyn, Caroline Lucas, Vince Cable and the Plaid Cymru leader in Westminster, Liz Saville Roberts.

They claim both candidates for the Tory leadership told parliament that the UK operated the most robust arms control regime in the world, but the appeal court found no independent British government audit of the Saudi bombing campaign in Yemen had been made.

The government is appealing against the decision, but has suspended sales to Saudi Arabia of arms that might be used in the war in Yemen.

In an unusual joint letter to the two candidates, the five party leaders at Westminster accuse the foreign secretary, Jeremy Hunt, and his predecessor Boris Johnson of showing “an absence of moral leadership responsibility and diligence during their cabinet tenures”.

They accuse the government of hiding behind platitudes in its response to a court of appeal ruling that ministers had acted unlawfully in clearing arms licences for use by Saudi Arabia. They write: “This is why our parties are calling for a full parliamentary or public inquiry to find out how that was allowed to happen, and which ministers were responsible for those breaches of the law.”

They write: “The reality is that there is mounting evidence that UK weapons exports have been used to kill civilians, pushing Yemen to the brink of catastrophe, and that the UK has gone to war on false pretences due to carte-blanche commitments in the past.”

“The UK government has traded at least €4.6bn of arms with Saudi Arabia since the war in Yemen began, supplying a regime that is directly responsible for indiscriminate attacks on civilians. The UN has reported 17,640 documented civilian casualties in Yemen so far; the majority of these casualties, estimated at 10,852, were victims of Saudi-led assaults.”

The letter also accuses Hunt of suggesting at one point that the UK would back military action in Iran, although he has recently said he cannot envisage circumstances in which the UK would join such a war.

The five claim “such a remark, similar to the rhetoric of President Trump, is incredibly serious and naturally has a bearing on what is already a highly volatile and potentially harrowing situation”.

They also accuse Johnson of incorrectly briefing MPs on the case of Nazanin Zaghari-Ratcliffe, who has been imprisoned in Iran on espionage charges. They claim: “Your false remarks were used in the trial against her. Her imprisonment has had a devastating effect on her life, her family, and her mental and physical health.

“Both of your words and your actions have had, and are continuing to have, serious and lasting consequences. One of you will be the next prime minister of the United Kingdom. We feel it necessary to remind you of the tragic consequences which are all too often the result of a failure to deal in facts.”

Blackford said: “The Tory government’s foreign policy for a long period of time has been overshadowed with controversy and stained by an approach often perceived as one of profits before peace.”