Age 2-3 : nursery school (not compulsory)
Age 3-4 : pre-school (not compulsory)
From 5 until 16, school is compulsory
Age 5-8 : Primary School
Age 8-11 : Junior School
Age 11-16 : Secondary/High School (exams taken during the final year are called GSSEs)
Age 16-18 : Sixth Form College / College of Further Education / Technical College (all optional) (Exams can be A Levels, AS Levels, NVQs and several others)
Age 18-21/22 : University / College of Higher Education (degrees)
We have both state-run and private schools - confusingly, the private schools are actually called "public schools". That's why sometimes you'll hear politicians etc referred to as "public schoolboys". That (usually) means they came from rich, upper-class families who could afford to send their children to the most expensive privately-paid schools.
It's probably not important but in the mid-80s there was a slight change in the age when we moved from middle (junior) school to high school. Until then, the age ranges (and school names) were:
First School - age 5-8
Middle School - age 8-12
High School - age 12-16
It was possible to move schools at the age of 11 if you took the "11 plus" exam. If you passed, you gained a place at a grammar school. These, at the time, were generally seen to give students a better education than a normal high school. As far as I'm aware, grammar schools don't exist any more.