Interesting choice - most families I know move out of Hackney (if they can) when kids need to go to state school.
If you can afford private, St. Paul's Cathedral has a small pre-prep, and prep school. Very nice. Easy to get to from Hackney - right beside Cathedral and just down the road from Bank.
At senior level, City of london School for Girls is always popular, and seems to turn out very well educated young women.
There are lots of private schools to choose from in Hampstead/Highgate, but difficult to get up there and back everyday from Hackney - traffic up the Holloway/Archway road often solid.
For state primary schools in the area - have a look at the league tables. If you find any you like the look of it is worth trying to find out how many children they lose at age 7.
My experience is that lots of middle-class families talk up the school till their child is old enough to move to prep/senior school, at which point a mass exodus occurs.
Or the less honest ones just move out of the area/London to access better schools, but say it is because of crime/pollution/quality of life issues...........