One word of advice - ignore all those people who tell you that children who are tutored to get into superselectives struggle.
I don't know how many applicants the schools that you are looking for generally have, but in this part of SW London your DC are up against 1500 + for 120 - 180 places (depending on which school.) If you think that probably the top third of those applying would cope perfectly well in a grammar school - particularly as those sitting the tests tend to be self selecting and "top table material" - that's 500 or so children, but only 120 (or so) of them will get places.
Is your child at state school now? If yes, then inevitably they will need extra help to cover the maths syllabus on time and if your primary is anything like ours, they will also need comprehension practice and practice on how to write a coherent piece in a set time - my DC had never written a timed "essay" at school before they sat their tests.
The other myth I would like to disspell is that superselectives are full of genius children - they are not! Of course they tend to be brighter than average but they also have to be hard working too. I have two at grammar and a third about to start and none of them is scary bright level and very few of their friends are. In fact, in relation to my youngest, three of his friends who I would class as scarily intelligent (particularly in relation to maths) did not get into any of the superselectives. All children need a big dose of luck on the day of the exam as well as being well prepared. And don't forget that no matter how bright or prepared your child is, there is always a chance that they just won't perform on the day, and there is nothing you can do about that. Always have a second choice up your sleeve - hope for the best but prepare for the worst!