Ms Eagle's bid to lead Labour had been put on temporary hold as the party's deputy leader, Tom Watson, held emergency talks with trade union bosses.
The main argument put forward is that the Labour Party is not ready to win the next elections under Corbyn's leadership.
Mr Horsfield, who is now travelling in Australia, decried the "disgusting" coup which saw most of Mr Corbyn's shadow cabinet resign and a vote of no confidence passed by 172 to 40.
Former shadow cabinet minister Angela Eagle has said she will challenge Mr Corbyn for the leadership on Monday - meaning a decision by the NEC will need to be made.
Corbyn denied reports he is willing to split the Labour Party if MPs do not back him, saying he simply had "an nearly philosophical discussion" on the topic.
"I'm a gay woman with strong, Northern, working class roots".
Watson said Corbyn's refusal to stand down meant there would be "no realistic prospect of reaching a compromise".
Corbyn's critics say that with Britain poised to negotiate an exit from the European Union that risks being more painful than many voters anticipated, Labour needs to present a strong, united alternative to the Conservative's ascendant anti-EU right wing.
Ms Eagle said: "This is not about splitting the Labour Party this is about uniting the party".
"Extraordinarily I received no notice of this statement before it was issued".
Southampton MP Alan Whitehead has written to party members explaining why he stood down from leader Jeremy Corbyn's frontbench team.
"I'm on the left, any party that I lead will be an anti-austerity party because what's happened in our heartlands is that they have been hit by six years of Conservative cuts piled up onto them", she told BBC One's Sunday Politics.
The leader of the UK Labour Party Jeremy Corbyn has said he is "disappointed" that Angela Eagle is launching a leadership campaign against him.
Mr Corbyn has insisted his name will automatically be on the ballot if a leadership challenge is launched against him and Mr McCluskey warned that if there was any legal attempt to prevent him fighting for his position it could risk a schism within the Labour movement.
"On Monday morning I will announce my candidature for leader of the Labor Party", she said. I heard you say it. I know Tom Watson has worked tirelessly in a bid to reach agreement and respect his view that he can not take this process any further. He said that the "real stresses" in the country are those faced by people struggling to feed their children or facing eviction by their landlords, calling on Labour MPs and the press to focus on that story.
Others see Corbyn's political appeal as too narrow, fearing that Labour will never win power under his leadership.
But how would a potential leadership contest actually work?
However, when Corbyn was elected leader, he secured 59.5% of the vote in the first round after a surge in support from newly registered activists.
Mr Woodland, who said that he spoke only in his capacity as a party member and not as a representative of the union, said MPs were guilty of a "childish and pedantic way of dealing with their disagreement with the leader".