I don't think you'd have any problem teaching any of the subjects in the lower grades, which is mostly what this is about -- you make it sound like you'd be required to homeschool your kids through graduate school. Certainly it requires some extra parental effort, as well as parents that work at home or otherwise have free time, but the actual subject matter for small children isn't rocket science.

At least in the US, my impression is that there are two main groups that gravitate to homeschooling:

1) Conservative religious types (mostly Christian) who are afraid that their kids will be brainwashed with secular values at a public school and start questioning their parents' authority, and

2) Liberal secular types who are afraid that their kids will be brainwashed into becoming mindless consumer robots who won't question authority or think for themselves.

Is homeschooling that uncommon in the UK?

I agree with your concern about the lack of social interaction with homeschooling.

Ken Strong