If you want to tutor during the school day, I wouldn't bet on home educated children coming out of the woodwork, especially not at KS1 and KS2. Possibly at KS4, but most tutors would be out of the budget of most home educators. I am a maths tutor and a home educator. I live in a major city (albeit not London) and as such know hundreds of home educated children. Literally. Most of my three children's friends are home educated and from all over the city and beyond. If I had to advertise (which I don't) I wouldn't even bother in home ed circles. By definition, most home ed families I know have to watch every penny due to sacrificing one income. They have to make lots of sacrifices and be very creative with how they provide an education for their children. Those that do find space in their budget for tutors, it tends to be for music, mfl, sports or other areas where they have little or no experience with which to facilitate their children's learning. Most home ed parents tend to be numerate and literate, and with a little help/advice can provide more than adequately for their children in these areas. Having said that, one service that I have often wondered about providing for the home ed community (and it has received a warm welcome when I've suggested it to friends) would be some sort of workshop or drop-in advice centre for parents (or parents and children together) where you could share your ideas and experience to help them to help their children. However if you have no experience of home education in your community, you would have to tread very sympathetically and respectfully and expect to learn as much from them as they will from you. I am a qualified and experienced teacher but I am often blown away by how rich an education my non-trained friends can provide. It's quite humbling.