Think very carefully before delaying entry to the independent system beyond eleven.
The two years from eleven to thirteen are a time when standards in the independent system really start to fly away from those in the state sector. By waiting until thirteen you will find your choice of independent school much reduced, since entry from the state sector to selective independents will be much more difficult at thirteen than at eleven leaving only the non-selectives to choose from.
Just last Saturday I was talking to a thirteen year old girl who moved into the independent sector this term - let us call her Imogen. The independent school she has joined is not really selective. Imogen is charming, intelligent and mature, despite having spent two years at a comprehensive; but she has found the transition at thirteen to be difficult. She mentioned two things in particular:
1. Whilst not unpopular, Imogen has yet to establish a group of real friends. The problem here is that like most non-selective independent schools, the main entry point to the school was at age eleven so friendship groups in Imogen's year are already well established. I am sure a girl like Imogen will find her place eventually, but just at present this troubles her.
2. Imogen had been the top pupil in her comprehensive school for mathematics so in recognition of her ability the independent school put her in its own top maths set, but Imogen finds she is now at the bottom of that set and struggling to keep up. This, I think, illustrates very well the point I made earlier about the academic progress made by independent schools in the 11-13 age bracket.
Moving at thirteen is not impossible - for example many prep schools don't teach Latin so most public schools are able to cater for new starters who have no Latin at that age - but it is certainly more difficult at that point than two years earlier.