Morgan, who has frequently called President Trump a friend, sparked criticism after he suggested the global protests following Mr Trump's inauguration were “vacuous” and attracted “rabid feminists”.
Less than an hour before McGregor was due to appear on the show, Morgan said the actor would be coming on the programme to discuss his latest film, the Trainspotting sequel, but McGregor changed his mind at the last minute.
“Was going on Good Morning Britain, didn't realise Piers Morgan was host. Won't go on with him after his comments about #WomensMarch,” McGregor wrote on Twitter.
Morgan, who is also editor-at-large of the US Mail Online, immediately hit back at McGregor’s no-show and suggested the actor should have appeared on the programme to openly debate the issues.
“Sorry to hear that Ewan McGregor - you should be big enough to allow people different political opinions. You're just an actor after all,” he said.
But Morgan later insisted they had no intention of talking to McGregor about the march. The controversial columnist said he would be writing an article about McGregor today and sending it to him for his approval.
Morgan’s comments about the Women’s Marches stoked controversy. As well as writing a column about the protest titled “Madonna and a bunch of famous, foul-mouthed nasty women let down ladies everywhere”, he also suggested the march was not about equality but was instead centred on “Trump-bashing”, “bomb threats” and “hateful jibes” directed at other women on Twitter.
“I'm planning a 'Men's March' to protest at the creeping global emasculation of my gender by rabid feminists. Who's with me?” he said.
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Both of McGregor’s daughters attended the protest and the actor expressed solidarity with the anti-Trump demonstrations which saw protesters take to the streets in 60 countries and on seven continents across the world to promote equal rights for women and defend marginalised groups.
“I'm with you in spirit today women of the world. My daughters are marching. I'm so proud to see this extraordinary power,” McGregor wrote on Twitter on Saturday.
President Trump has a record of making demeaning, sexist comments about women. This includes boasting that when you are a star you can grab women “by the pussy” in a leaked 2005 tape, calling comedian Rosie O’Donnell a “fat pig”, and saying former Fox News journalist Megyn Kelly had “blood coming out of her wherever”.
McGregor has been outspoken about his political beliefs in the past. In the aftermath of the Brexit vote, he made headlines when he accused Boris Johnson of behaving in a “spineless” manner after his shock announcement he would not be running for Conservative leader. He also rebuked Mr Johnson for campaigning to leave the EU and then not dealing with the consequences.
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