The following research by Paula Rothermel of the University of Durham explores the aims and practices of home educating families from diverse socio-economic backgrounds:
Home-Education: Rationales, Practices and Outcomes - Paula Rothermel
http://www.dur.ac.uk/p.j.rothermel/Research/Researchpaper/BERAworkingpaper.htm

Home-education: Comparison of Home and School educated children on PIPS Baseline Assessments.
http://www.dur.ac.uk/p.j.rothermel/Research/ESRC/PipsBaseline.htm

You can read more of Paula Rothermel's research here:
http://www.dur.ac.uk/p.j.rothermel/

Publications

Free Range Education: How Home Education Works by Terri Dowty

Home Educating Our Autistic Spectrum Children: Paths are made by walking by Terri Dowty (editor), Kitt Cowlishaw (editor)

Natural Learning and the Natural Curriculum by Roland Meighan
Learning Unlimited by Roland Meighan

Educating Children at Home by Alan Thomas

Teach Your Own by John Holt
How Children Learn by John Holt
How Children Fail by John Holt
Learning All The Time by John Holt

Dumbing Us Down: The Hidden Curriculum of Compulsory Schooling by John Taylor Gatto

Deschooling Society by Ivan Illich