I think if you live in K & C you are very restricted in choice unless you are CofE or Roman Catholic. If the former you have Chelsea Academy (mixed) or the two girls schools in Westminster, St Marylebone or Greycoats. Chelsea Academy is not very academic though.
St Thomas More (mixed) is a very nice RC school in an awful building.
If you are non religious and live in North Ken you have only one choice next year, Kensington Aldridge which hasn't opened yet. Holland Park has changed its admissions criteria to select on proximity. Chelsea Academy has some non religious places but you have to attend an RBKC primary and be fairly near.
Sion Manning, RC girls, still has an awful reputation but it seems to have improved a lot and the girls seem well behaved on the street and public transport.
Holland Park is OK. Not the great institution the hype suggests and very cultish; both in terms of the Head and SLT, and a group of golden kids at the top of the pile. Some teaching great, some very bad. They have trouble keeping staff because they work them into the ground. My DD likes the social life but hates the actual school ethos. Constant criticism and not being good enough.
I don't know enough about LBHF schools to recommend. Obviously Lady Margaret is great but you have to be very near. I have heard the Hammersmith Academy is awful (6th form) and West London free not up to much at all. I know a girl at Fulham Cross, likewise Burlington Danes, both very happy there. Hurlingham and Chelsea sadly is the school to avoid, likewise Phoenix based on anecdotal evidence.