The Good Schools Guide contains details about all schools, including state.
The Independent Schools Guide contains details about independent schools only (funnily enough)
GSG website has a free bit and a paid subscription bit. The paid subscription has more info, and you can choose to pay for a month or year subscription. There is lots of info on the free part of the website, and it has a good search facility. I haven't noticed any schools missing from the website.
ISG website is free but very little info about each school (nothing that you couldn't find on wikipedia or the school's own website). There seemed to be a lot of schools profiles missing from the website.
I am a teacher and have used the free part of the GSG website to find about about schools I am interested in working in.