You could also google The Good Schools Guide. You can search for independent schools in your area on their website and while it is a subscription service, you will be able to get the basic data (school names, addresses, contact details) free of charge. I have just tried myself and it came up with a list of 12 independent schools around Cardiff (type in Cardiff in the search box and scroll down a little bit to get to the options selection box on the left-hand-side of the screen where you can chose what sort of school you are looking for)
You would only have to pay if you wanted to read detailed reviews of the schools. I did sign up once, just for a month while they had some sort of an offer on, only paid a few pounds and it was well worth the money.
NB. I guess your thread title was supposed to be 'independent' school?