Ms Waters, the director of Sharia Watch UK who co-founded anti-Islam group Pegida UK together with Mr Robinson, made her comments on Newsnight where she appeared alongside rival candidate Peter Whittle.
Ms Waters, who has previously branded Islam “evil”, said she did not think Mr Robinson had any thoughts of joining the party, but that she would not be opposed if he did want to.
“There is a leader’s discretion. I think I would leave it up to party members. For the record, I woudn’t lift the ban on groups such as the BNP (joining Ukip),” she said.
Mr Whittle said the party’s constitution banned individuals who have been members of far-right groups, including the EDL, from being accepted as Ukip members.
But Ms Waters said: “A lot of people around the country support those sorts of people. A lot of people think exactly the same way and have nobody representing them.”
If Ms Waters is elected later this month, some members and supporters believe it could spell the end of the party, which has seen its fortunes fade since the Brexit vote and the resignation of former leader Nigel Farage.
No fewer than 18 of the party’s 20 MEPs have said they will leave the party if Ms Waters wins on her controversial anti-Islamification platform.
Ms Waters, who was prevented from standing as a candidate in the last general election by then-leader Mr Nuttall, said: “First of all, I don’t think they will all leave. I think there’s an awful lot of misunderstanding about what I’m saying.
“A lot of people seem to think I have two heads and when they realise that I don’t, that I just want to speak – we ought to be able in this country to say what we think about religion, and the problem we’ve got is that we pussyfoot around, and we spend so much time agonising about not saying the wrong thing.”
She added: “This is how millions of people in this country feel and they’re waiting for someone to articulate it for them.”
Mr Whittle, the party’s current deputy leader, argued it was vital to keep the focus on delivering Brexit for the British people rather than on the issue of Islamification.
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