UKIP said in a statement that, after a discussion of "recent press coverage" of the leader, "the committee took the decision to hold a vote of no confidence in the leadership of Henry Bolton".
Bolton has said he ended "the romantic side" of his relationship with Marney after the Mail on Sunday newspaper published text messages to a friend in which she called black people "ugly" and said Prince Harry's fiancee Meghan Markle would "taint" the royal family.
"I shall not be resigning as Party leader", Bolton told reporters in Folkestone, southern England.
Since Farage stepped down as party leader in the wake of the Brexit referendum, UKIP has had three leaders, including Bolton, plus a pair of caretakers.
"Instead, during the next four weeks I shall be calling for the coordination and mobilisation of all Leave campaigns, to ensure that the government delivers full independence from the European Union in all areas of government and administration and I shall be calling for the Party itself to mobilise to support this agenda".
Deputy leader Margot Parker, assistant deputy leader Mike Hooker, London spokesman Peter Whittle, immigration spokesman John Bickley, trade spokesman William Dartmouth, culture spokesman David Meacock, communities spokesman Tim Aker, Brexit spokesman Gerard Batten, sports spokesman Bill Etheridge, liabilities spokesman Star Anderson, work and pensions spokesman David Sprason and MEP Jonathan Arnott have stepped down.
Mr Bolton continued that Ukip's ruling body "as presently constituted, is unfit for objective and has severely handicapped the Party's progress and political delivery for some years, as all recent UKIP leaders will attest".
Under the UKIP rules, an emergency general meeting (EGM) must be staged within 28 days to endorse or reject the no- confidence vote.
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The latest resignations follow a meeting of the party's NEC over the weekend in which its members unanimously backed a vote of no confidence in Bolton.
'He should now resign from Ukip immediately so we can get on with rebuilding the party without further distraction.
"The NEC requires significant and urgent reform".
The departure of charismatic leader plunged party into a weird succession of internal fights that, on one occasion, came to hands, with a candidate hospitalized after being knocked down in European Parliament's quarters for a punch by a fellow of rows.
"In a single phrase, it is time to "drain the swamp".
The committee does not have the power to remove the former army officer - that can only be done by a vote of the party's membership.
UKIP is also struggling financially.
He told reporters that he had urged the NEC not to expose the party to the financial and political cost of removing him as leader and holding yet another leadership contest.