There's nothing wrong with Sevenoaks, from a pupils' and parents' perspective, far from it, it's a lovely school. Ex-h and I didn't particularly like teaching there, but that's a different story, and the biggest issue was just because boarding didn't suit us.
It is a very good school and I would be happy for my own dc to go there (on scholarship, obviously) if we were still local. Teaching is mostly excellent, academic support is good, pastoral support is decent, and of course the facilities and cocurricular offering are superb and the setting beautiful. All I meant is that there's schools in London whose teaching and learning is as good. The OP will have to weigh up the setting against the travel, because the quality of education at Sevenoaks overall is very good, but not uniquely so, and the question is whether it's worth the extra distance.
Again, when I said it's not that difficult to get in, I meant in comparison with other independent and grammar schools within commuting distance. Clearly you have to pass the entrance exams and interview, you don't just walk in, but IME someone who is reasonably academic stands a good chance. The level of entrant we got was not, IME, significantly higher than for comparable schools. I wasn't directly involved in admissions, ex-h was.
OP, do you know much about IB? I would suggest investigating it before making a decision. Sevenoaks gets very good results with it and it is popular, but it doesn't suit every student. It would be worth looking at whether you think it would be a good fit for your dd.