"are the reports something you have to compile yourself or are they simply a form you complete with evidence of things you have been doing?"
That depends whether you listen to the LA or to the home educators
. Many LAs will try to insist on HE parents filling in forms, accepting home visits, and presenting "evidence" of their children's learning. The law does not support them in demanding such things. In fact, the 2007 government guidelines on home education, which are still in force, specifically state that none of this is necessary. That document is very useful: www.gov.uk/government/publications/elective-home-education .
IMO the trouble with filling in LA forms is that you are tacitly accepting their value judgements about education. Given that LA staff tend to have a school background and little or no training in home education, their ideas about how it should be done are not likely to coincide with yours. For example, their form may ask how many hours a week you spend educating your child, a question which presupposes that education is a timetabled activity distinct from the rest of the child's life. The number of hours I have timetabled in advance for overtly "educational" activities is tiny, shockingly tiny if you think that is the only way learning happens. But if I look back at the last week, it's clear that my child was learning for far more hours than those.
Last night, on an evening in the "school holidays", she was in the room while I watched three Spanish documentaries about deep-sea creatures. The English subtitles were on. Her dad and I kept pausing the video to talk about geology and tourism and various other things. She appeared to be playing with her stuffed toys, but it became evident that part of her attention was on the video and our discussion. She was trying to decode the English words (she is learning to read), to understand the maps, and to pick out some Spanish. Primarily she was interested in the sea creatures, and the rest appeared to be a means to that end. How on earth would I categorise that under subject headings on a school-style form? And that is just the obvious stuff: most of what she learns is done very quietly and I don't even know where or when or how it happens.
So if I were to write a report describing my child's education, it would be based on my understanding of how she learns and would mention her interests and the resources available to her, giving some examples of what she has done in the past. It would look nothing like a school report.
Once the LA has some information from you, they can contact you with any specific questions they may have, and you can address those. So you don't have to send them a highly detailed document in the first instance. A few sides of A4 should be enough to satisfy them.