AHEd's Figures on Abuse Rates in the Home Education Community (From FOI requests re LA responses - less than half national average):
Abuse rate in HE Community 0.32%
Abuse rate nationally (all children) 1.30%
LAs' total numbers of EHE children range from Thurrock 0, Knowsley 6 and Rutland 9 right up to the big ones: Essex 576, Devon 599 and Kent 662.
With such a large standard deviation it isn't good to extrapolate but doing it would give a total for all 152 LAs of 19,800 EHE children known to LAs.
AHEd's Wiki Page
Summary of Statistics used in Badman Report - Received FOI on August 20th.
FOI'd Information from LAs re Concerns over Suitable Education
Annexes 1 and 5 via FOI. (We are assuming they are Mr Badman's unpublished statistics from his indepth questions to 25 LAs.)
1. Total elective home education (EHE) population
• 12,300 children were registered EHE in the 90 LAs that responded to our questionnaire. Approximately 35% were of primary age, 65% of secondary age.
• Can therefore assume approximately 21,000 EHE children in the country (1).
• These data relate to known, registered children only. We know that to be an underestimate and therefore one could assume these figures may be higher.
5. Known to social care 
25 of the 90 LAs asked responded (28% response rate)
*Based on the data we have from the 25 LAs, the average (median) proportion of EHE children per LA known to social care is approximately 7%. We estimate there are approximately 3% of children (5-16 years) known to social care in maintained schools. 
*Within the 25 LAs for which we have data, there were 477 registered home educated children who were currently known to social care.
*On average (median) 7 children per LA were known to social care.
*Extrapolating to the national level (150 LAs, this means around 1350 home educated children are known to social care in some capacity (6.75%)
(1) Known to social care includes Sections 17, 37, 47 enquiries.
(2) Using 2005 data (the latest available), these are approximate figures and include disabled children."
NB: "Known to social care" is not the same as being on a social services register for being at risk of abusing a child. Known to social care here means families that will have been referred to services or have used services under sections 17, 37 and 47 of the Children Act 1989.
Section 17 deals with the provision of services to children in need, and has nothing to do with whether that child is at risk of abuse from his parents.
Sections 37 and 47 will include all families who are referred to social services, whether or not there was any actual risk of abuse. The home education community suffers from an extremely high rate of spurious referrals to SS, eg: for no other than that the referrer didn't realise that HE is a legal option. Yet these families, once referred, remain "known to social care". It does not mean they are on an "at risk register".
See also a statistician's comments on these statistics on AHEd's wiki page.
The Independent (on the now debunked Badman claim that HE children are twice as likely to be on at risk registers.)
Links for National Abuse Rate
Dani's Request for clarification of stats.