Julia is not a spy. She repeatedly tells Winston in their conversations in the apartment above the antique store that she doesn't care about revolution or overthrowing the party. She is not an Inner Party member, or she wouldn't be able to associate with Winston.
She is intrigued with sex, with living her life for her own pleasure (fully knowing that if she is caught, it could mean death for her and for her current partner), and with being smart enough to engage in these activities without the Party's knowledge. She tells Winston that she has had many partners, and some of them were with Inner Party members. This is one of the reasons, Winston states, that he loves Julia so much.
One wonders why Julia has been able to get along with her activities secretly for so long. It is my contention that had she not connected with Winston, she would still be at her extra curricular activities. Until Winston, one can summise that Julia's partners were like she is...not looking to overthrow the Party, but seeking sexual partners only for the pleasure, adventure, and thrill it provides. When she finds Winston (who openly hates the Party and envisions its downfall), they both are captured and sent to the horrors of The Ministry of Love and Room 101.