Do I have to follow the curriculum?Short answer. No.
In school circles "the curriculum" is both revered and loathed in equal measure. A curriculum is (like say the national curriculum) where someone outlines what they think your child (or children in general) should know. In certain educational systems like the Charlotte Mason method, or Trivium you can buy different interpretations of what they think would currently make a curriculum. The issue with this is that it might be wildly inappropriate for your child. National curriculum in particular are not written by educators at all but by political people in Government who have vested interests (sometimes financial ones) in what children learn (or don't learn). One of the greatest freedoms of HE is that you don't have to follow someone else's idea of what your child "should" know. They can learn what they find interesting, what you think is important to know and what they might need in their lives. LA's tend to prefer national curriculum because they tend to come from a school background, but they don't have to be "appeased". As long as you are educating, from unschooling to Montessori to your own unique HE master piece the curriculum is not important.
You can of course borrow and use parts of sections of curriculum should you wish too (we recently had a look at the English G.C.S.E texts and my daughter is reading them (some she has read before). Some Charlotte Mason curriculum can be bought as well as other alternatives and again they can be useful, up to a point.
The issue comes down to standardisation. What a child should know, and how deep that knowledge can be is often determined by age. Age is an unreliable marker, as children do not tend to grow in neat little bits constantly but in slow-sluggish bits and sudden bursts. The physical development and mental ability are not the same thing and the emotional capacity are another thing entirely.
By eight years old and off her own bat, my daughter had read 67 books out of a 100 Classic books in literature. It was on her Nintendo D.S. Yet while some she adored a lot she "didn't get it". Jane Eyre and Pride and Prejudice seemed weird and pointless stories concerned with marriage and status. Though able to read these books she didn't yet have the emotional intelligence to connect to the text. I wonder if the reason I loathed Charles Dickens was because I was forced to read it at 11 years old and I had no context or understanding of Victorian Britain.
Had I had some context, some knowledge around what we were reading, or just read it a year or so later I might have had a different reaction.
The other thing is curriculum tend to get bogged down in not only what is taught, and when but HOW they are supposed to learn. This means a vast majority of learners never discover how they learn. Or feel "thick" because they simply are not wired to do it a certain way. This is the greatest failing of curriculum. It fails to allow children to discover and learn in their own way. It fails to place value on the natural ability of children to learn. In some circumstances getting a wrong answer, the way they taught you, will give you a better mark/grade than getting the right answer a different way.
Some curriculum remove the child out of the equation entirely. They are written for ease of testing and marking, not learning or child development. The industry behind this is worth a lot of money and is based more on agriculture than child development. It is also about control. What someone is "allowed" to learn means that their are subjects that they are not "allowed" to learn. From human rights, taxes, the laws of their own country or state, health and well being, histories that they would rather keep hidden, a curriculum is as much what it excludes as what it includes.
Home education is far too important to take seriously.