Brexit party politicians appeared on programmes that have hosted conspiracy theorists and promoted the views of prominent figures on the hard right, an analysis has found.

Nigel Farage’s party, which won the most UK seats in the European elections only months after its launch, is still scoring above 10% in the polls and could prevent prime minister Boris Johnson securing a majority in a snap general election.

It has steered away from the hard-right policies pursued by Farage’s former party, Ukip. However, several MEPs have appeared on shows that have broadcast conspiracy theories and retweeted messages from alt-right figures, according to the anti-racism campaign Hope Not Hate. It also found MEPs had retweeted prominent figures on the far right.

The investigation found that the MEPs Ann Widdecombe and David Bull had appeared on the Richie Allen Show, an internet radio programme that has hosted antisemitic conspiracy theorists and Holocaust deniers. Widdecombe appeared on 10 April, just before Kevin Barrett, a contributor to the antisemitic conspiracy theory magazine American Free Press.

Bull was a guest on 30 April, tweeting that the experience was a “pleasure”, linking to his interview via the website Conspiracy Daily Update. He was followed on that episode by Lana Lokteff, the American white nationalist broadcaster.

Stuart Waiton, a Brexit party hopeful for Dundee West and an unsuccessful MEP candidate in Scotland, appeared on the show five times between June 2018 and May 2019.

Farage appeared in an online documentary, Bilderberg: The Movie (2014), alongside a number of conspiracy theorists. He tells the film: “I’ve tried very hard not to believe in conspiracy theories, but I’ve been here now for over 15 years, and I can see there is a move towards supranationalism ... I’ve got to know over the years the Van Rompuys, the Schulzes, you know, the Barrosos, even the Junckers, the Timmermans, and it’s completely clear, they actually want to destroy the nation state as a unit.”

Brexit party campaigners in the Brecon and Radnorshire by-election in August. Photograph: Ben Birchall/PA

Farage and his MEPs Michael Heaver, Nathan Gill and Martin Daubney have shared the tweets of Jack Posobiec, a promoter of the “Pizzagate” conspiracy theory, which claimed a Washington pizzeria was a front for a paedophile ring that stretched to the top of the Democratic party. Other figures to be retweeted by Brexit party MEPs include Mark Collett, a former BNP figure, Stefan Molyneux, a far-right Canadian YouTuber, and Mike Cernovich, who has kept a blog promoting men’s rights, anti-feminism and misogynist pick-up artistry.

Matthew McGregor, campaigns director of Hope Not Hate, said: “The Brexit party has come from nowhere to be the potential kingmaker in the next parliament. These figures – some of whom promote racists, appear on conspiracy theory radio shows, and push divisive rhetoric – could be MPs in a few weeks. The idea of Nigel Farage having a say over the future direction of the country used to be a joke, but it’s time to take his dangerous and divisive party very seriously.

“Farage says he wants to dissociate himself from Ukip’s far-right positioning. If so, he needs to act quickly to sack any MEP or parliamentary candidate who has promoted far-right figures and dissociate his party from these dangerous conspiracy theorists. If he doesn’t, it will be clearer than ever that his party should face a concerted campaign against them at the general election.”

A Brexit party spokesman dismissed the findings, saying: “This has to be the biggest false start in archaeology since the discovery of Piltdown man [a hoax in which bones were presented as the fossilised remains of an early human]. A series of tangential, transient retweets. There again, if that is the worst they can find, then their donors will be upset with all the waste of research funding.”

Polling of voters sympathetic to the Brexit party suggests they are deeply concerned about multiculturalism, wary of Islam and overwhelmingly want to leave the EU without a deal: 84% want a no-deal Brexit.

The polling found that 71% believe a wide variety of backgrounds and cultures has undermined British culture, 67% said on the whole immigration has been a bad thing for Britain and 63% think Islam is generally a threat to the British way of life.

They also have strong anti-establishment views: 83% think that political correctness is used by the liberal elite to limit what we can say and 79% think that political correctness is causing the police and media to deliberately play down the ethnic background of some child sex abusers.

The figures are based on polling by YouGov of 934 people with a favourable view of the Brexit party. The survey was carried out online from 26 April to 1 May.