In my area of S London, we have fantastic primary schools and appalling secondaries (unless you are RC and even then...). I was a school governor at one and it was just depressing. Celebrating just over 40% getting 5 GCSEs isn't great.
I went through all our local ones results very carefully - you can have schools where the overall results are bad but there is still a small cohort that are getting a good haul of GCSEs and A levels at high grades. In these schools that is not the case, and they rarely send any children to university - let alone RC or Oxbridge.
It's one of the reasons that we are moving - we can't rely on the standards improving and there are no private schools or even semi-selectives in the area.
I went to grammar school myself - but took Common Entrance 13+. I've no idea what it's like now, but then it was a case of doing a minimum of 1 paper (and in some subjects 2 or 3 papers) in English, Maths, History, Geography, RE, MFL, Latin, Science etc as well as VR and NVR over the course of a week, and the final result was an average of the scores in all papers .This meant that kids who were mathematically minded could drop marks on humanities and vice-versa, plus it wasn't completely dependent on being on form for 1 single day.
In my mind, this is a much fairer way of selecting - and at 12, children are a bit more mature than they are at 10. The disadvantage of course is that state primaries seem to concentrate far more on English and Maths than on other subjects. I was at a prep school which had a very fixed curriculum and taught all subjects to the same level of importance whether that was English or Geography.