The conversation about Islamic extremism should begin with “Saudi Arabia and other Gulf states that have funded and fuelled extremist ideology,” Jeremy Corbyn has said.

The accusation is common: that the House of Saud is allowing a flow of money to finance ISIS. But the Saudi government has completely rejected the “false allegations”, dismissing them as a “malicious falsehood”.

We can’t answer this one with absolute certainty, since any financing is highly secretive. All we can do is weigh up the documents and research that are currently available.

How strong is the evidence?

Perhaps the most powerful indication of Saudi’s financial links with ISIS can be seen in the cache of emails leaked from the office of Hillary Clinton, who was US Secretary of State from 2009 to 2013.

The messages, published by Wikileaks, contain an unambiguous statement by her campaign chairman, John Podesta:

“We need to use our diplomatic and more traditional intelligence assets to bring pressure on the governments of Qatar and Saudi Arabia, which are providing clandestine financial and logistic support to ISIL and other radical Sunni groups in the region.”

This wasn’t the first time US officials had made this claim. In 2009, Wikileaks published diplomatic cables from the US State Department which spelt out the same concerns.

“Donors in Saudi Arabia constitute the most significant source of funding to Sunni terrorist groups worldwide,” the documents said. “While the Kingdom of Saudi Arabia (KSA) takes seriously the threat of terrorism within Saudi Arabia, it has been an ongoing challenge to persuade Saudi officials to treat terrorist financing emanating from Saudi Arabia as a strategic priority …

“More needs to be done since Saudi Arabia remains a critical financial support base for al-Qaeda, the Taliban, LeT, and other terrorist groups, including Hamas, which probably raise millions of dollars annually from Saudi sources.”

A third Wikileaks file appeared to show a private speech that Hillary Clinton made in 2013. In it, she said: “The Saudis and others are shipping large amounts of weapons – and pretty indiscriminately – not at all targeted toward the people that we think would be the more moderate, least likely, to cause problems in the future.”

While the Wikileaks files are widely regarded to be genuine, FactCheck cannot verify the accuracy of the claims within them. However, given the repetition of similar statements, it certainly seems that people in the highest ranks of US government have had good reason to believe money is flowing between Saudi Arabia and ISIS.

Indeed, the former US vice president, Joe Biden, once spoke off-message by accusing Saudi Arabia and other Gulf states of pouring “hundreds of millions of dollars and tens of tons of weapons into anyone who would fight against Assad.” He explained: “The people who were being supplied were al-Nusra, and al-Qaeda, and the extremist elements of jihadis who were coming from other parts of the world …

“We declared [ISIS] a terrorist group early on. And we could not convince our colleagues to stop supplying them.”

In other countries, politicians have been more vocal about these concerns. For instance, in 2014, the Iraqi prime minister Nouri al-Maliki accused both Saudi Arabia and Qatar of supporting and funding terrorists.

“I accuse them of inciting and encouraging the terrorist movements,” he said. “I accuse them of supporting them politically and in the media, of supporting them with money and by buying weapons for them.”

However, just because the Saudi government is not doing enough to stop the flow of money to ISIS, that doesn’t necessarily mean the cash is coming direct from the government itself.

In fact, research by the Washington Institute said there was no credible evidence of this at the moment. This is probably because Saudi Arabia is fearful of the threat ISIS may pose to their own country, it said.

But the report added that Saudi government “has taken pleasure in recent ISIS-led Sunni advances against Iraq’s Shiite government, and in jihadist gains in Syria at Bashar al-Assad’s expense”.

It added: “It would not be surprising to learn of limited, perhaps indirect contact, logistical coordination to further Sunni positions in Syria and beyond, or leaking of funds and materiel from Saudi-supported rebels to ISIS.”

“Arab Gulf donors as a whole – of which Saudis are believed to be the most charitable – have funneled hundreds of millions of dollars to Syria in recent years, including to ISIS and other groups,” it said. “Riyadh could do much more to limit private funding.”

The reality of ISIS financing is complicated and messy. It’s not as simple as just donations from wealthy backers; research suggests the militants have made a fortune from oil reserves which it controls.

An investigation by the Financial Times in 2015 estimated they earned $1.5m a day from oil, and even sold to the very rebel groups they were fighting.

It’s worth noting that other countries are implicated too, such as Qatar and Kuwait. So although Saudi is accused of funding the group, it is not alone.

Why don’t we stop them?

The Wikileaks files suggest there have been western efforts to “bring pressure” on Saudi Arabia to end its support for ISIS. But that seems to be the extent of it.

Publicly, both the UK and US keep up very good relations with Saudi Arabia.

Theresa May visited the country in April, to “further strengthen the UK’s relationships in the Middle East”.

A government report about the trip said: “She made clear that they are a close and important ally and that we will continue to work closely in a range of areas, particularly on counter-terrorism where UK-Saudi co-operation is vital.”

May has said it’s in the UK’s “security and prosperity interests” to maintain a good relationship with Saudi. “By working with them, we are helping keep British people safe,” she said.

And, in America, the CIA has described Saudi Arabia as being “among our very best counter-terrorism partners globally”.

Western politicians have financial reasons to stay close to Saudi Arabia too. It is the world’s largest exporter of petroleum, with huge reserves of crude oil. Plus, both the UK and US also make a fortune by selling weapons to Saudi Arabia.

Government documents show that British arms companies have been granted 636 military export licences for Saudi Arabia in the last five years. These were worth around £5.2bn in total. Meanwhile, America has just signed a $110 billion arms deal with the country, including planes, ships and bombs.

There’s also a balancing act in terms of security and intelligence.

Supporters of western policy say that – despite these concerns – the state is an increasingly rare and important ally in the Middle East.

Theresa May has said a good relationship is in “British national interests”.

But although the political and diplomatic solution may be far from clear, it seems that the concerns over Saudi money being channeled to ISIS are real and serious.

What does the UK government say about it?

Not much. David Cameron commissioned a report into foreign funding of terrorist groups, back in 2015, but the Home Office has admitted it may never actually be published. It is thought to focus on Saudi Arabia and is said to be “very sensitive”.

However, both Labour and the Lib Dems have called for the report to be released. Jeremy Corbyn said: “We have to get serious about cutting off the funding to these terror networks, including Isis here and in the Middle East.”

Without this report, we cannot say for sure what the UK government knows about Saudi funding to ISIS.

But it seems likely that – although the House of Saud may not be directly financing terrorists themselves – there are almost certainly some difficult and worrying questions to answer.

Update: the Saudi ambassador writes…

After we published this story, the Office of the Saudi Ambassador to the UK sent us this statement: