I think the Daily Mail headline is clickbait-y and I don't think she's "blaming" Madonna at all. What I took from this was that she wanted to be like Madonna when she was a popstar because she looked up to her so much, but the difference was Billie was a teenager (15 when she started). This lead to her being oversexualized by the industry before she was even 18, and she's spoken in lengths about having traumatic experiences behind the scenes during those times. She's not blaming Madonna for that.
She clearly doesn't having a problem expressing her sexuality as an adult, i.e. Secret Diary of a Call Girl, but it's different when record execs were pushing her, a teenage girl at the time, to be more sexual.