My eldest DD was just accepted at City of London School for Girls. I don't know if other Mumsnetters would consider it "highly selective" or not.
She is coming from a state primary that has never sent a child to City or even tried. It is a good state school though, and they have been supportive of the application, giving her time off school for the exam and the interviews and writing a thoughtful reference to City.
She always did well in school and was a "top table" student without any tutoring. She had/has loads of extracurricular activities including sport and music. We let her watch scads of tv and muck around until the end of year 5, when the penny dropped that she was actually quite behind in a very competitive field despite being at the top of her class. We tried to tutoring her ourselves, but it just didn't work. In the end, we paid someone to do it for us. She was so much happier to listen to someone who wasn't us, and happier to do practice papers for them too.
Once she had some practice writing stories and essays, and learning long multiplication and fractions, percentages, ratios, etc., she was able to close the gap. For 6 months she saw a tutor once a week and did an old entrance paper as practice once a week. She did one paper over Xmas break. Then the week before her North London Consortium exam she got up half an hour early to do bits of old exam papers as practice. It was her idea. I don't know if it helped, but I think it gave her a sense of purpose and control.
She plays the violin in the school orchestra and participates in a load of sports. I am not aware of the schools taking any notice of this. It's my impression that they are not bothered about musical ability unless you have reached grade 5, at which point they do take notice.
Sorry for rambling. What I am trying to say is, if your DD is around the top 5% academically, she should easily be able to gain a place. But, she will still need some form of tutoring to bring her up to the standard of the test. The extracurricular stuff is nice to have, but I didn't notice much emphasis on it from the schools. The exception being, if they are at scholarship level, which is very high and requires a long term time commitment to reach.
The most important thing at all these schools is the entrance test. Download an old example from the school's website and do it yourself. It gives you the best idea what you are up against and the gap you have to fill.