It was a sobering exercise realizing that there's a fair amount of Orwellian and Huxleyan prophecies in our modern world, but we tend to focus more on the 'scarier' Orwellian ideas.
What Orwell feared were those who would ban books. What Huxley feared was that there would be no reason to ban a book, for there would be no one who wanted to read one. Orwell feared those who would deprive us of information. Huxley feared those who would give us so much that we would be reduced to passivity and egotism. Orwell feared that the truth would be concealed from us. Huxley feared the truth would be drowned in a sea of irrelevance. Orwell feared we would become a captive culture. Huxley feared we would become a trivial culture, preoccupied with some equivalent of the feelies, the orgy porgy, and the centrifugal bumblepuppy. As Huxley remarked in Brave New World Revisited, the civil libertarians and rationalists who are ever on the alert to oppose tyranny “failed to take into account man’s almost infinite appetite for distractions.” In 1984, Orwell added, people are controlled by inflicting pain. In Brave New World, they are controlled by inflicting pleasure. In short, Orwell feared that what we fear will ruin us. Huxley feared that our desire will ruin us.
The world in the book is a strange blend between pure decadence, socialism and consumerism. The society is atheist, but worships Henry Ford. There is a communist equality, but it is enforced through strong castes. Everyone is happy and free, but the world controllers act as an oligarchy of dictators. Science is valued, but only the right kinds.
I believe the book is popular among intellectuals because, like Fahrenheit 451, the society shown has an anti-intellectual and anti-knowledge streak.
Sadly, the entire western world is just a lot more authoritarian than it was during Huxley and Orwell's time.
That said, Huxley's critique of the left (if it can even be called that) didn't seem like one based on any left-wing principles or ideas. I really don't know where he was coming from on that. It really felt like it could have been written by some cheap right-wing tabloid. Maybe that's why it was so popular.
Huxley was critiquing Hitler and especially Stalin. Is that your idea of "the left"?
I wish I had I had a copy in front of me, so I could give you specific examples. It's been a long time since I read it.