The only thing you have mentioned they cant do is have a disciplinary policy and not follow it. If they have a document they should make it available (s3 or 6 of the employment act) and follow it
The ACAS site is here:
http://www.acas.org.uk/index.aspx?articleid=2177
sort of lands you in the middle of the section on Discipline
There is quite a lot of reading
and you will have to have your appeal in within x days ( 7 or 20 or 28)
but remember if yours is a small employer, then these things are informal so you should be able to add things to your appeal - unless of course their printed policy expressly forbids .