No idea how many people there are, but it's a lot and seems to be growing rapidly. It's hard to guess at figures because there is no requirement for parents to inform anyone that they are home educating. The LA does get informed when a child is taken out of school. Two years ago, Oxfordshire County Council reported to a government reviewer that it was aware of 287 home educated children in Oxfordshire. That figure would include children who had been withdrawn from school and remained in the area, but it would miss out most children who had never been to school as well as most of those who had moved to the area while already being home educated.
Not everybody is part of an organised home ed group; some parents aren't aware of them and some don't feel the need for them. However, there are over 500 people on the local home ed email list. Anyway, my girls (aged 11 and 5) have no shortage of friends both in and out of school!
People have various reasons for home educating. According to home ed organisations, the most common reason for a child to be withdrawn from school is bullying. But I also know a number of children who simply weren't happy at school. In the last few years with the shortage of school places in the area, I think there have been more people doing home ed because they weren't happy with the school they were offered.
As for me, I just felt four was too young for my older daughter to be in formal education and so I thought I'd wait and send her at six or seven... but by the time a few years had passed, she was doing so well that there seemed no point sending her to school at all unless she wanted to go. Her little sister has special needs and I never seriously considered sending her to school because it was obviously not right for her.
Many home educating parents seem to have found the whole experience much easier and more pleasant than expected, and so we are often keen to suggest it to other people who might like to try it. It's straightforward to withdraw a child from school and also straightforward to return her to school if you decide home education isn't the right way forward. The only time I usually recommend that people should be cautious about leaving school is if they like their child's school and it is oversubscribed, in which case there is a real risk of not getting back in. But it sounds like that isn't a concern in your case.