It is sadly a too common story that even good private schools, even in the affluent Hampstead and Camden areas are giving false praise about their pupils' standard or progress in Mathematics. For example, if I am teaching Arithmetical Fractions in Year 10 or 11 it is a sign something is seriously wrong and the schools don't seem to mind even in the run up to the new harder GCSEs.
It may seem attractive when a school offers coaching as it may well be all inclusive, but please remember it is cheap or free for a reason. It is far better to have a more expensive tutor who does the job properly and in fewer sessions than a cheaper tutor with very limited progress. It may even be better financially in the long term because of the shorter period of having coaching.