"Her words were blatantly racist and there should be no room for that in UKIP", wrote party member Jack Penny on Twitter, after calling Marney the "Wallis Simpson of UKIP", referring to the American divorcee with alleged Nazi sympathies that King Edward VIII married after abdicating.
UKIP chairman Paul Oakden said: "In light of messages that have been brought to my attention, I have taken the decision to immediately suspend her party membership pending an investigation".
UKIP MEP Bill Etheridge called for Mr Bolton to resign.
Ms Marney later apologised "unreservedly" for the "shocking language" she used in the messages.
In a series of highly offensive messages sent to a friend, Ms Marney reportedly said Harry's "black American" fiancee would "taint" the Royal Family blood line and pave the way for a "back king".
"It is quite apparent that he does not have the experience, the nous, or the correct advice to deal with the issues that he faces".
UKIP's London Assembly Member Peter Whittle called the remarks "disgraceful" and called for her expulsion.
Earlier this month, Mr Bolton announced in a letter to UKIP supporters that he had started a relationship with Ms Marney after splitting from his wife, but denied a "clandestine affair".
"UKIP does not, has not and never will condone racism", he said.
Everything announced during today's Nintendo Direct Mini
Mario + Rabbids Kingdom Battle will also be getting a new story update where players will be able to take control of Donkey Kong. The release dates vary, but Nintendo is aiming to ship all of this content to you in the first half of the year.
Other party members instead resisted the idea of sacking their leader, concerned about the future of a party that has endured three leadership elections and a shrinking popular support in recent months, since founder Nigel Farage stepped down after the Brexit referendum in 2016 delivered a majority for the "Leave" side for which he had campaigned.
He said he had already made clear on social media that he had recently been spending time "with somebody who has become increasingly important to me".
He tweeted: "Utterly false!"
A push alert that warned of a ballistic missile heading straight for Hawaii and sent residents into a full-blown panic on Saturday was a mistake, state emergency officials have said.
The party chairman, Paul Oakden, said the leader had "some hard decisions" to make.
Meanwhile former UKIP leadership candidate Ben Walker called for Bolton to quit, accusing him of having "deeply flawed judgement". "The woman just in shot is a BBC staffer". When informed that one of her messages were racist, she replied by saying "so what?" The opinions I expressed were deliberately exaggerated in order to make a point and have, to an extent, been taken out of context.
On her Twitter profile Ms Marney describes herself as a model, actor and journalist, as well as a Brexiteer. "But I think it's a very serious problem if it wasn't that, or even it was, it shows that we have problems in the system that can cause major disruption and panic and anxiety among people in Hawaii".
The former Army officer caused national outrage after he left his wife Tatiana Smurova for the young model he met only weeks before Christmas.
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