Three MEPs have resigned in a little over two months, amid infighting over leader Gerard Batten’s shift towards the far right.
Robinson is currently banned from becoming a member by party rules, but has been inciting his supporters to join Ukip so they can influence its policies.
The national executive committee (NEC) delayed a potential ballot on Robinson’s membership until after Brexit in March, but Mr Batten responded by making him an “adviser” on grooming gangs and prisons.
Defectors believe Mr Batten will be further emboldened by surviving a vote of no confidence mounted by supporters of former leader Nigel Farage on Sunday.
Suzanne Evans, Ukip’s former deputy chair, said as she resigned that the result was the end of the road.
She described being increasingly alarmed in recent months by the "perverse direction" in which Mr Batten was taking Ukip, and saw the vote as the party’s last hope.
Ms Evans accused the NEC and remaining MEPs of turning a blind eye to the "obvious attempts by Gerard and Robinson to orchestrate a Momentum-style takeover”.
“I would never have joined Ukip as it stands today, obsessed as it is with becoming a successor to the British National Party (BNP) and the English Defence League (EDL), and putting an increasingly hostile and vicious focus on attacking the Muslim community en masse,” she said.
A spokesperson for Ukip said Mr Batten was disappointed in Ms Evans’s decision.
“However, he must weigh up the loss of a few individual members such as Ms Evans with the more than 8,000 new members who have joined the party since he became leader,” a statement said.
Robinson, whose real name is Stephen Yaxley-Lennon, founded the EDL in 2009 but left four years later.
The anti-Islam activist now styles himself as an “independent reporter” and has capitalised on a surge of publicity over his imprisonment earlier this year to forge political ties across Europe, the US and Australia.
Mr Batten has appeared at several “Free Tommy” protests – including one where Batten labelled the prophet Muhammed a “paedophile” – and has repeatedly called Islam a death cult.
He has been pushing for Robinson to be allowed to join Ukip, but the party's rules exclude former members of the BNP and EDL.
Mr Batten said Robinson did not need to be a member to become his adviser, amid outrage last month, and the pair would speak at a “Brexit betrayal” march in London on Sunday.
Robinson has called on the more than one million people who follow his Facebook page to join Ukip and has been directing them to its registration page.
One post from 27 November was commented on by hundreds of supporters who claimed they had joined because of Robinson.
“By joining we can influence the party,” Robinson told them. “Members that join with similar views shape the direction.”
He assured them that as the EDL had no formal membership, it was impossible to prove, and claimed that followers would be able to vote him into Ukip in a potential ballot in March.
One jubilant Robinson supporter wrote: “You will be in charge one day and I’ll be there.”
An MEP who quit Ukip in October told The Independent he feared that Mr Batten was keeping the seat warm for Robinson.
Bill Etheridge said the current leader, aged 64, was not getting any younger and had previously voiced an intention to retire.
“The fact Robinson has been taken on as an adviser without even being a member would suggest he is going to have a senior role,” he said.
“He will be involved in the clique around Gerard and certainly I would have thought in time he would have ambitions to taking on the leadership … I think Mr Batten might be keeping the seat warm.”
William Dartmouth, a hereditary peer and MEP who quit Ukip in September, raised similar concerns.
“Mr Batten is setting Robinson up to be the leader,” he told The Independent. “Resigning members have been replaced by people who support Mr Robinson and his ilk.
“This has entirely been led by Mr Batten and he's got no mandate to do it. His conduct is an utter disgrace.”
Mr Batten was appointed interim leader of Ukip in February, after predecessor Henry Bolton was ousted over his affair with a model who made racist comments about Meghan Markle and later apologised.
“He stood on a ticket of continuity and there was no election,” Lord Dartmouth said.
“Since then he has completely hijacked Ukip and turned it into an anti-Islamic party.”
Asked whether Ukip was in the grip of an identity crisis following the EU referendum, the MEP insisted it still had a role to play in an increasingly uncertain Brexit.
Lord Dartmouth claimed that Mr Batten’s views on Islam were previously not known among the membership and that he rarely gave speeches until his appointment.
Mr Etheridge said he had intended to stand as leader himself but was told by Mr Batten that he would be leasder for a year "and entirely focus on Brexit”.
“From that point on his focus became more and more the issues around Tommy Robinson and multiculturalism,” he said.
“He was approached by several people who asked him to keep to the remit of Brexit, but he just carried on.
“He marginalised many of us who had been Farage supporters and made it clear he was taking the party in his own direction.”
Mr Etheridge said figures he saw before his resignation showed that party membership has risen, but he believed that those with more moderate views had been leaving in droves.
“When Gerard goes round saying Islam is a death cult, he doesn’t leave anyone in doubt of his stance,” he said.
“The membership has changed dramatically in its character and style, as has the direction of the party.”
Speakers at Ukip’s party conference in September included right-wing bloggers recently welcomed as members such as Mark Meechan (Count Dankula), who is best-known for being prosecuted over a video showing a pug performing Nazi salutes.
An “interim manifesto” presented at the event included proposals to create Muslim-only prisons and repeal hate crime laws.
Mr Etheridge, who has joined the Libertarian Party, said the manifesto was not discussed with anyone – "apart from a small circle of Gerard’s friends” – and shocked other members.
“I tried to argue the case and rally support around people nudging him back in the right direction, but the ferocity of support for Gerard from new members made it impossible to change,” he said.
Patrick O’Flynn, another MEP who quit Ukip last week, said he had also tried to persuade Mr Batten to maintain his focus on Brexit and abandon an apparent and growing fixation with Robinson.
“Instead he has done the opposite,” he said in his resignation statement.
Defectors acknowledge that there has always been a “school of nationalism” within Ukip but insisted the party had a broad membership united around opposition to the EU, and took active steps to keep far-right extremists out.
They pointed to the 2017 rejection of the virulently anti-Islam leadership candidate Anne Marie Waters and numerous expulsions of councillors over their views.
Mr Etheridge said Mr Batten appeared to have saved Ukip temporarily from financial ruin and secured a small but significant net membership increase.
“By calling people to rally round his very strong and extreme views on certain matters, he will have a strong membership, but he’ll also frighten off the general public who might have been inclined towards Ukip in the past,” he warned.
“Ukip should be on at least 15 per cent in the opinion polls and it’s not. I believe it is because his views are making the party so marginal that normal voters just don’t want to touch it.”
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