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Alex, 40, expressed his views to Piers, 56, in a fiery debate where Alex defended the Duke and Duchess of Sussex's interview with Oprah Winfrey.
The on-screen row saw Piers briefly walk off the set, before it was announced later on in the day that he had quit the programme.
While many supported Alex for speaking out against Piers, he has also faced racist trolling - forcing him to "step away" from social media.
In a piece written for The Telegraph, Alex explained: "Three weeks ago I took part in a television debate about the decision of the Duke and Duchess of Sussex to publicly reveal the racism they claimed to have suffered as members of the royal family, and the impact on their mental health.
"Since then I have been subjected to relentless racism myself on social media. I haven't announced it... but I have been forced to step away from Twitter and Facebook myself, because it was getting too much. I am a strong person, but I am not made of steel.
"These are just the past few weeks of my own, very much lived experience of racism in Britain."
As well as discussing his own upbringing in the UK as a mixed-race man, Alex continued that he has experienced "dozens" of occasions where he or his friends have "faced racism".
"Not all racism is caught on camera," Alex continued. "Between myself and friends we have dozens of examples of where we have faced institutional racism throughout our lives: in some of their cases, losing out in the workplace and restricted opportunities."
He added that Meghan Markle's story, where she claimed a senior royal asked how "dark" son Archie was going to be, and said she felt "suicidal" after she married into the Royal family, had "resonated" with him.
"From a similar experience around the concern of a baby's shade of colour to the devastation of laying to rest someone very close to my heart just three months ago, who had those same suicidal thoughts," he explained.
"Whilst appearing to be a Royal problem, it felt so personal to me."
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