The Henry Jackson Society said there was a "clear and growing link" between Islamist organisations in receipt of overseas funds, hate preachers and Jihadist groups promoting violence.
The foreign affairs think tank called for a public inquiry into the role of Saudi Arabia and other Gulf nations.
The Saudi embassy in London says the claims are "categorically false".
Meanwhile, ministers are under pressure to publish their own report on UK-based Islamist groups.
The Home Office report into the existence and influence of Jihadist organisations, commissioned by former Prime Minister David Cameron in 2015, has reportedly yet to be completed amid questions as to whether it will ever be published.
Critics have suggested it could make uncomfortable reading for the government, which has close and longstanding diplomatic, security and economic links with the Gulf, particularly Saudi Arabia.
BBC security correspondent Frank Gardner said he understood the report was "largely finished and sitting on Theresa May's desk", but there was probably a reluctance to publish it because of "embarrassing" content…