.
I have to say I thought you were *** if you had admitted an offence.
However you say that the events happened abroad,
and so it raised the question about whether events that are not a crime are cautionable.
Since an appeal would be on how the system went wrong and not on the facts ( JR) it would be appealable - BUT judicial reviews start off at £2000, and it is clear you dont have that sort of money.
http://ukcriminallawblog.com/2013/02/22/cautions-adults/
has this:
If I have accepted a caution can I appeal?
Generally no. There is no appeal body as such, but you can Judicially Review a decision to administer (see R v Metropolitan Police, ep Thompson [1997] 2 Cr App R 49). This is a very expensive procedure and is hard to win. You have to show that something has gone badly wrong, such as there not being a proper admission. A good example from 2012 showing the issues involved, and the difficulty in winning an argument, see the case of Lee v Chief Constable of Essex Police [2012] EWHC 283 (Admin).
So in short the answer is "yes-maybe" if you have money like Bill Gates....