I am sorry to hear the bad news.
In the months and months of preparation - on the worst practice papers (tired, distracted etc) child has only ever been one or two questions away from a solid pass - these results are way off.
Please bear in mind that there are very few published practice papers that are of the same difficulty level as the real 11+, so the results of practice tests (even the official familiarisation papers) may not always be indicative of the final result.
Is 'marking error' a possibility?
Mitasol has pointed you at link on how to request a re-mark, but I would just add that the papers are marked by an electronic "optical reader", and errors are very rare. If a child has failed to rub out an incorrect answer completely, the reader may have picked that up in error, but otherwise the marking is generally very accurate.
I have seen the thread re: Data Protection rights - does this mean I can get access to both test papers and answer sheets to assess for myself?
It would seem that appealing is discouraged given the marks
It is not discouraged on any score, but on scores of 112/112 I am afraid the chances of success are very slim unless you can provide exceptionally strong academic evidence by way of school reports that mention high ability, predicted Level 5 SATs, good past test scores (CATs, reading tests, etc) and a high standard of work in school books.