Just in case it's of interest, I recently went to a meeting with the head of a top independent S London selective, for parents of children who had passed the exam to get in. He congratulated us all on having bright DC and then chuckled, 'who of course none of you tutored at all'.
He knew about the tutoring. He was fine with it. What concerns me is that these schools openly protest that tutoring is not required and there are some well-intentioned parents out there with DC at state schools who believe it. Their DC are very unlikely to have covered the whole syllabus in Maths and English, and they are up against prep school DC who do VR and NVR papers every day before assembly. Some, like Newgirl, may be lucky enough to have a maths club that does 'puzzles' (aka NVR familiarisation or tutoring, at school) but most don't.
What's important is to know what the school you're applying to asks for in its exam, what level of attainment is needed to secure a place, whether your DC can realistically reach that with or without help, and if with help, what are the gaps that need plugging in their knowledge or skills. Then work out a schedule of practise that suits them, with tutors, or through school or through home tutoring. Dead simple.
I strongly recommend people ignore the posters who gush: 'My DC got in with no effort at all.' It's stealth bragging. Yes, some DC are natural born geniuses. These schools are not filled with such DC. There truly aren't enough fo them to go round. They are filled with top set, level 5 & 6 bright kids who work hard and have been well prepared for the exam.
My DH is off the scale clever - got top marks in 11= when he was small, then got off the scale marks in the US scholarship NVR style testing when he applied for a Fullbright. I'm nowhere near that clever, but sharp enough to get into Oxbridge. Our DC have grown up in a naturally inquisitive and academic home and were both in top sets with anticipated high 5s and 6s at end of Yr 6. They both needed tutoring.