David Cameron should order a proper inquiry into the funding of jihadism or face questions about the closeness of the Conservative party to “rich Arab Gulf individuals”, Paddy Ashdown, the former diplomat and ex-Lib Dem leader, has said.

Lord Ashdown, who was a high representative to Bosnia and for the UN in Afghanistan, said there had been a “failure to put pressure on the Gulf states, especially Saudi Arabia and Qatar, to stop funding the salafists and wahhabists and secondly to play a larger part” in the campaign against Isis.

He said this and other instances in which Cameron had failed to have a proper inquiry into the funding of jihadism in Britain had led him to “worry about the closeness of the Conservative party and rich Arab Gulf individuals”.

He called for Cameron to order an inquiry into funding of jihadism and added: “If not, I think we’re entitled to ask: why not?”

As evidence of Tory closeness to Saudi Arabia, he mentioned the case of the prime minister ordering an inquiry into the Muslim Brotherhood that “came to a conclusion unhelpful to the Saudis” – that the group are not extremists. The report is still to be published despite being finished some time ago.

He said any plan put forward by Cameron needed to include pressure on Gulf states to stop the funding of Sunni jihadism and to play a greater role in tackling Isis. “If we are sending their pilots in, why aren’t [they]?” Ashdown said.

The former Lib Dem leader also called for the UK to tackle Isis as a priority over demanding the end to the Syrian regime of Bashar al-Assad, who is thought to have used chemical weapons on his own people.

“I think we should be impatient about the removal of Isil and I think we should be more patient about the removal of Assad,” he said.

Ashdown’s demand for an inquiry into Saudi funding of jihadism echoes calls by Labour leader, Jeremy Corbyn, to examine the arming of Isis and role of funds from Saudi Arabian sources.

“Who is arming Isis, who is providing safe havens for Isis? To get there you have to ask questions about the arms everyone’s sold in the region, the role of Saudi Arabia in this. I think there are some very big questions and we have to be careful,” he told ITV1’s Lorraine programme last week.

Saudi Arabia, the UAE, Jordan and Bahrain are all still listed by US Central Command as taking part in airstrikes against Isis but they are not taking a lead in the campaign. Saudi Arabia in particular has come under criticism for not doing enough to tackle support for Isis from some of its wealthy citizens.