There are four separate places in which John the Savage repeats Miranda's words "Oh brave new world" from The Tempest.
As background, in The Tempest, Miranda has spent her life from a very early age on a deserted island, with her aging father as the only other human she remembers having seen. Therefore, when she glimpses the group of handsome men who have been shipwrecked on the island, she is so impressed with the beauty of mankind that she is overwhelmed with rapture and says "Oh brave new world..."
In the first instance of quoting from The Tempest, Bernard Marx has invited John to come back with him to the World State. As John thinks of this opportunity and of Lenina, he is overwhelmed with happiness and quotes Miranda, saying very sincerely:
How many goodly creatures are there here! How beauteous mankind is! ... O brave new world...
A few moments later, when he finds out Lenina isn't married:
“O brave new world,” he repeated. “O brave new world that has such people in it. Let’s start at once.”
The irony, of course, is that Lenina being single means nothing, as nobody marries in the World State. She is never going to fall in love with him, because she has been conditioned never to get attached to any one person.
In the second instance, John is disillusioned with what he sees in the World State. He has been told all his life by Linda that it is wonderful, but he perceives that the people here are little more than slaves. When he sees identical groups of Delta minuses and Epsilon morons working in a factory, he says this quote again, with bitter irony:
“O brave new world .” By some malice of his memory the Savage found himself repeating Miranda’s words. “O brave new world that has such people in it.”
The scene at Park Lane Hospital for the Dying, where he has gone to see Linda, marks the third instance when John quotes The Tempest. He sees mass groups of ugly and dehumanized identical Delta twins and makes the comment again:
“How many goodly creatures are there here!” The singing words mocked him derisively. “How beauteous mankind is! O brave new world.”
After seeing Linda, he is grief-stricken, both because she is dying and because he now realizes she has lived her life brainwashed by the state. Feeling extremely bitter, he notices the mass of Deltas again, this time waiting for their soma tablets, and has an outburst at how terribly sad and degraded this world is:
“O brave new world, O brave new world.” In his mind the singing words seemed to change their tone. They had mocked him through his misery and remorse, mocked him with how hideous a note of cynical derision! ...“O brave new world!” Miranda was proclaiming the possibility of loveliness, the possibility of transforming even the nightmare into something fine and noble. “O brave new world!”