As far as I am aware, they just want to check your not driving something dangerous. Having your battery properly strapped down and a fire extinguisher on board is a requirement at some places i've been, but as this is a big 'general public' doo and not a particularly 'hard core' course, so I doubt it will be too strict. I believe there will be routes for the less adventurous though, as well as some more challenging bits! This will be my first trip to Abingdon though so please dont take this as gospel, I aint seen it yet.
p.s. Just spoke to the Chief Marshall for the event and apparently, unlike Stoneleigh, there is no booking or limits to the off road course. You can spend all weekend driving round and round if you like!!
p.p.s The is a video of someone driving round the course on the Abingdon4x4 web site.