The education system is a bit complicated here, but at 5-6 your daughter will have to go to a 'primary school'.
At that age she has the following options.
A state run primary school which take children from 4-11. Some of these can be very good.
An private (paid for) primary school from 4-11. There are not loads of these but there are a few. Some of these can be good but don't assume that just because you pay it's automatically better than a state school.
A Prep School. A private school for children from 4-13. Generally bigger and with good facilities. Children move on to private secondary schools at 11/13 when they leave.
An 'all through' private school for children aged 4-18. There are a few of these, they usually have very good facilities. It means you don't ever have to worry about where your child is going to school.
if you can't afford or don't want to use a private school then you will use state schools. Most of us do!
If this is the case then your child will go to primary school until 11. If you live in an area where there are grammar schools (free schools for academically able pupils) your child can take an exam to see if they can get a place in one of these. The schools are very popular and hard to get into.
If you don't get a place in grammar school there are state secondary schools. Again, some of these are good, others less so!
I hope that helps?
I can't help with specific schools but I hope I explained the system.
If you want good state education and have a choice about where to live, I would personally find a non grammar area with good schools as this takes the pressure off!