It was announced last weekend that Mr Young, a right-wing journalist who has helped establish a number of free schools, is to join the board of the newly-created Office for Students.
The move sparked an angry backlash after it emerged Mr Young had previously criticised wheelchair ramps in schools as a sign of “ghastly inclusivity” and claimed working-class students at Oxford University were “universally unattractive” and “small, vaguely deformed undergraduates”.
It has since come to light that Mr Young also posted a number of comments on social media about the appearance of female MPs, described a gay celebrity as “queer as a coot” and wrote about visiting a bar full of “hardcore dykes”.
In one tweet from 2011, he remarked on a session of Prime Minister’s Questions between David Cameron and Ed Miliband by saying: “That’s quite a cleavage behind Ed M.”
A year later he wrote: “Serious cleavage behind Ed Miliband’s head. Anyone know who it belongs to?”
In 2013, he responded to criticism of his previous comments by saying: “Women who display a lot of cleavage shouldn’t then complain when men notice them.”
The free school campaigner also commented on a photo of him next to a woman by joking that he “had my d*** up her a***.”
Labour said Mr Young’s comments about women were evidence of “misogyny” and made him an inappropriate person for a government role.
Asked for comment, Mr Young told The Independent: “I’m neither misogynistic nor homophobic. I’m a strong supporter of both women’s rights and LGBT rights.”
In a post from 2009, he criticised the appearance of television presenter Claudia Winkleman, writing: “What happened to Winkleman’s breasts? Put on some weight, girlie.”
The same year, he attended the Emmy Awards ceremony and wrote: “The women here are smoking hot. There should be an award for Best Baps.”
Most of the tweets appear to have since been deleted.
The conservative commentator, who writes for The Spectator magazine, has also written about having dressed up as a woman in order to seduce lesbians. In the article, he described meeting gay women he called “hard-core dykes”.
And in 2010, he described gay singer George Michael on Twitter as “queer as a coot”.
Dawn Butler, the shadow minister for women and equalities, called on Ms May to sack Mr Young over the tweets.
She said: “By any measure, this is a shocking appointment by the Prime Minister. These comments show that Toby Young is completely unsuitable for this role.
“If she fails to rethink this appointment, the message Theresa May is sending to students is that under the Tories, misogyny and homophobia will not just be tolerated but rewarded.”
His appointment to the Office for Students was engulfed in further controversy after it emerged that the Department for Education had wrongly claimed Mr Young held teaching posts at Harvard and Cambridge.
He told The Guardian: “I taught undergrads at Harvard and Cambridge and was paid to do so but these weren’t academic ‘posts’ and I’ve never made that claim.”