The National Curriculum came into being as part of the Education Reform Act 1988.  It applies to Local Authority State Schools in England, Wales and Northern Ireland.  State-funded academies have a certain amount of autonomy when it comes to the national curriculum.  It doesn't apply to independent schools (although they may choose to follow it) and it doesn't apply to home educators.

It's aim is to "be "broad and balanced." It enables standard testing and league tables.

The subjects included in the national curriculum are:
English (KS1, KS2, KS3, KS4)
Maths (KS1, KS2, KS3, KS4)
Science (KS1, KS2, KS3, KS4)
Computing (KS1, KS2, KS3, KS4)
PE (KS1, KS2, KS3, KS4)

Geography (KS1, KS2, KS3)
History (KS1, KS2, KS3)
Music (KS1, KS2, KS3)
Art and Design (KS1, KS2, KS3)
Foreign Languages/Modern Foreign Languages (KS2, KS3)
Citizenship (KS3, KS4)
Welsh  (KS1, KS2, KS3, KS4 - in Wales)

In addition, all state schools are also required to make provision for a daily act of collective worship.  They must teach religious education to pupils at every key stage.  There is also a statutory obligation to provide Sex education to pupils in secondary education which parents can opt their children out of.

KS4 Entitlement Areas
There are a number of subject areas that a school is obliged to offer at KS4, but are NOT compulsory national curriculum subjects.  This is because pupils in maintained schools have a statutory entitlement to be able to study a subject in these areas.  These areas are:
The arts (comprising art and design, music, dance, drama and media arts), design and technology, the humanities (comprising geography and history) and modern foreign language.