I have been through this three times and can honestly say we never used tutors. To me, it can be counterproductive because no tutor is going to understand the way maths is taught at the school, for instance - or specifically what they have been doing that week. So, if they are teaching things one way and the school another, it just overloads the kids and confuses them. As for things like VR and NVR, the papers can be found on the internet or the Bond papers or whatever, and it's just a case if working through. You don't need to pay someone £50 per hour to watch your child do Bond papers!
Having said this, mine were all in a prep (albeit a non-selective, very mixed ability one). I do recognise that state schools may well offer zero 11 plus exam exposure and so parents feel the need to have something going on outside school. Also mums / dads don't have the time quite often, so throwing money at a tutor can take away some anxiety and make them feel they are at least doing something. Often the tutor is more use as support for the mums, rather than actually helping the kids in any tangible way.
At the prep mine were at they had a Maths paper as homework during the week and they did a book called 'Schofield and Sims' on the weekend. Every week there would be a comprehension task too. VR and NVR was one lesson per week in school. All this started around in the summer term of Year 5. It felt like a lot of work as it was.
I had one go through LU. I can't fault the academic side if things and we are very grateful for that, but my personal take, looking back (and this is only a personal view!) is that socially, it's a tough environment there for many. Retrospectively, DC describes it as "aggressively West London." DC actively avoided unis such as Durham and Edinburgh which have large groups of what they call "West London private school types" who often tend to stay in these groups once at uni. DC was mostly very average at LU, but came into their own in about year 10 and got into Oxbridge where it's more diverse (socially). General impressions are the uni people are more 'normal' and 'less neurotic' as there are all types from all over the U.K.
I have DC at G&L and I don't really know what the difference is, but they have been much happier socially. I would say they have thrived socially, rather than survived socially, if they makes sense. It feels somehow 'kinder' there. But again, purely anecdotal and I'm sure other girls have had different experiences. A lot of it is just luck really.