There are huge variations in the amount of tutoring that children at schools like SPGS will have both before joining and when in the school.
Overall these schools are interested in potential, so want to have an idea of educational background. Close to a decade ago we knew a girl who had no play dates for six months before the SPGS exam, the mum was quite open about it, and a lot of tutoring, both before and after school. She ended up struggling and left after a couple of years. DS was surprised, at a comparable school, at how much tutoring some of his peers had. (One bright boy from east Asia spent every vacation at a tutorial college - not unusual where he came from.)
But it all came out in the wash. DS and friends, who relied on the school to educate and the prep school to prepare, were not top of the year but have done very well at University. Some others, where there was more pressure to achieve whilst at school, became burnt out, or found it difficult to switch to self-motivation.
It’s a long haul. They will be in FTE until at least around the age of about 22. Pacing is vital, as is the idea that education and learning can be fun.
The only exception is that kids at state school might benefit from a bit of external preparation with content and how to cope with exams. And it is worth considering extra support for kids with problems in either maths or English, as these are building blocks for other subjects. Aside from that time outside school is probably better spent broadening experience, is sport or music, or simply hanging out with friends and family. Schools like SPGS work best if the fit is natural. London has lots of good alternatives.