The group numbers only a few thousand people in New Zealand, and its members are not allowed to vote in elections.
Yet they have made headlines over allegations of murky political lobbying tactics in what began as a row over spending by political parties during the 2005 election.
The Exclusive Brethren has been accused of pouring large amounts of money - reportedly close to the election budget allowed by a political party - into a clandestine publicity campaign that attacked left-wing parties and urged voters to take a moral, conservative line.
The group was then accused of seeking to influence post-election negotiations by aggressively lobbying minor political parties to form a coalition with Mr Brash's centre-right National party.
Most disturbingly, private detectives claimed they were hired by the group to dig up dirt on the private lives of senior politicians in the Labour party, including the Prime Minister Helen Clark and her husband.
The reclusive Exclusive Brethren - which shuns contact with the media - has said very little against the allegations, except to claim that any campaign literature supporting conservative policies or the hiring of detectives was the work of individuals, not the group.
Don Brash initially denied any knowledge of the group's election pamphlet, but later admitted meeting members of the group both before and after the election.
His resignation came days after he sought an injunction to prevent the publication of emails he said were stolen from his computer.
This injunction resulted in halting the publication of a book, The Hollow Men, which claims to expose the inner workings of the National Party, including its links with the Exclusive Brethren.
Author Nicky Hager says he accepts Don Brash's word that he did not know the injunction would have an impact on his book's publication - but does not believe it played no part in his resignation.
The book, he says, contains documentary proof - provided by disgruntled members of the National Party - of secret alliances with right-wing groups such as the Exclusive Brethren and of broken election spending rules.
"The book is about the gap between what the electorate was told during and after the election and what was going on behind the scenes," he said.
So who exactly are the Exclusive Brethren?
The group has its roots in the Plymouth Brethren - an evangelical movement that began in Ireland in the late 1820s before splitting into two main branches, the Open Brethren and Exclusive Brethren.
The Exclusive Brethren are thought to number around 40,000 worldwide, and are headed by a Sydney businessman, Bruce Hales, who is called the Elect Vessel and the Man of God.
As their name suggests, the group practices a strict separation from the world, generally associating only with each other and avoiding outside influences such as TV and the internet.
But despite this, members have earned a reputation for good business skills and a low rate of dependency on state welfare schemes.
Their businesses are mainly linked to agriculture, horticulture and transport.
Peter Lineham, a religious history expert at Auckland's Massey University who has relatives who are members of the Brethren, says it is their business interests, as much as their religious beliefs, that would be a motivating factor behind any move towards political lobbying.
Like all small business people, they need a world of de-regulation and lower taxes, he says, adding that their interests in the agricultural sector would naturally pit them against the Greens.
"Since they can't vote - and their numbers wouldn't influence the outcome anyway - they are seeking to influence the election in other ways," Mr Lineham says.
Part of the controversy arises from the fact that the leaflet campaign they are said to have orchestrated before the 2005 election looked and read like National party literature, but there was no indication of who had originated the material.
Peter Lineham believes the storm has been fuelled by the fact that the group did not publicly defend itself.
"What the Exclusive Brethren did during the election campaign was not unlawful. But I think the fact that they will not talk back has allowed the election-spending debate to be moved into different territory."
Marion Maddox, a religious and politics expert at Victoria University in Wellington, says the Exclusive Brethren's involvement became a "noose around the neck" of the National party.
But the group's involvement in politics is nothing new, she adds.
"They took out newspaper adverts supporting [Australian Prime Minister] John Howard and also ran adverts in state newspapers. None of it was picked up until after the election," she says.
In fact, it appears the Exclusive Brethren has also been involved in political campaigning in the US, Canada and Sweden - other countries where it has significant numbers of members.
Australia's Green Party accused the group of carrying out a campaign that included an anti-gay agenda during state elections in Tasmania in March.
It has also warned that the same thing could happen in forthcoming elections in Victoria - due to take place on Saturday - and in New South Wales next March, and called for a Senate investigation into the group which was turned down.
But the mood in New Zealand at least has turned against them.
"There is not a lot of sympathy for the Exclusive Brethren here," Peter Lineham says.