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.