0640 GMT July 24 2017
The Henry Jackson Society said there was a "clear and growing link" between extremist organizations in receipt of overseas funds, hate preachers and groups promoting violence, BBC reported.
The foreign affairs think tank called for a public inquiry into the role of Saudi Arabia.
The Saudi Embassy in London said the claims are "categorically false".
Meanwhile, ministers are under pressure to publish their own report on UK-based extremist groups.
The Home Office report into the existence and influence of organizations, 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 Persian Gulf Arab nations, 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.
The Henry Jackson Society is a foreign policy think tank that advocates the robust spreading of liberal democracy, the rule of law and the market economy.
At the top of the list, the report claims, is Saudi Arabia, the UK's closest ally in the Middle East and biggest trading partner.
It alleges individuals and foundations have been heavily involved in exporting what it calls "an illiberal, bigoted Wahhabi ideology", quoting a number of examples.
In a minority of cases, the report alleges institutions in the UK that receive Saudi funding are run directly from Saudi Arabia, although in most instances the money appears to "simply buy foreign donors' influence".
Britain has a close, longstanding and sometimes controversial relationship with Saudi Arabia.
Annual bilateral trade is worth billions of pounds, UK exports to Saudi Arabia, notably in defense, employ thousands of people in both countries, and there is close cooperation on counterterrorism.
But UK and US-supplied warplanes and munitions are being used by the Royal Saudi Air Force to bomb targets in Yemen, resulting in civilian casualties.
Saudi Arabia also has a much-criticized human rights record. This has prompted calls from some, including Labour leader Jeremy Corbyn, for an arms embargo on Saudi Arabia.
But Theresa May has spoken of the economic and security benefits of this alliance and has pushed for closer ties with Britain's Persian Gulf Arab partners.
In a statement, the Saudi Embassy in London said any accusations that the kingdom had radicalized "a small number of individuals are baseless and lack credible evidence".
And it pointed out that the country has itself been subject to numerous attacks by Al-Qaeda and Daesh terrorist groups.
It added: "We do not and will not condone the actions or ideology of violent extremism and we will not rest until these deviants and their organizations are destroyed."
The Home Office said it was determined to cut off the funding of extremism but it declined to comment on the think tank's report.
The report's release comes at a sensitive time with Saudi Arabia, the UAE, Bahrain and Egypt all accusing Qatar of supporting extremism – a charge the report says is hypocritical.
Endorsing the report, Labour MP Dan Jarvis said it shed light on "very worrying" links between Saudi Arabia and the funding of extremism and he called for the government to release its report on foreign funding.
May, who visited Saudi Arabia in April, has insisted the UK's historic relationship with the desert kingdom is important for British security and trade.