Winston and julia turned willingly themselves over to O'Brien and the Brotherhood because, they were made to believe that the Brotherhood fought the same course as them.
Reasons for believing O'brien and. Brotherhood.
(1)Wine: in the book, its phenomenal that only rebels drank wine. Seeing red wine in O'brien's house made them believe he was a rebel.
(2)Determination: winston and Julia had been rebeling in secret, finding an organisation with the same motives as theirs, made them join
They do like that because:
firstly they are defenseless which means that they are physically defeatable by the party, and mentally unprepared to what is happening in front of them. In short, they have no idea why they were discovered.
Secondly they know that this day would happen to them and although they try to escape there are no places to stay and no one would sincerely help them. Besides, what would you do if the place is already surrounded by the thought police.
Both Winston and Julia are determined to be rebellious. Julia expresses this through her outright sexuallity, the fact that she doesn't care who she sleeps with, she merely does it for the carnal pleasure, as well as the forbidden nature. Winston is slightly similar, in that he also desires to rebel (although he goes about it in a different nature and is eventually distracted and placated by the physical relationship with Julia) The existence of "The Brotherhood" is to Winston sometimes his only encouragement. Multiple times in the book, he implies his want for the Brotherhood to see what he has written in his journal, he also fantasizes about what life would be like in the Brotherhood.
The two of them are also cruely tricked by O'Brien. We learn later in the book that the only desire of the higher and highest party members is pure, cold power. "A boot stamping on a human face— forever." So we know that Party members have no inhibitions when it comes to trickery. O'Brien has no respect for Winston or Julia, and does not feel any sort of companionship or need for sympathy towards either of them. All of that allows O'Brien to pull such tricks as the turned off telescreen, the vocal confession, and the fake book.
This is a fun question! Think about it: what else are they to do at this point? The plot leads to this reaction as well since they both know it is inevitable that they will be caught. I sense an almost longing to be caught from these two characters from the start. And with Julia's past and connections, it leaves the reader with that unsettled feeling that perhaps it was planned that way from the beginning from her end. Also, as plot development goes, we see the demise of what little is left of Winston's spirit, even his humanity. It also leads the reader to the inside workings of the Brotherhood, and supports the overall mood of the novel.