The reason given is completely unfounded. An appeal only seems to allow you to repeat the claim, not to point out their error. What is there to do?
I've had this exact same problem. I had 2 train cancellations within 4 days of each other. I submitted both claims for a delay between 30-59 minutes (as my trains are every 30 minutes) but SWR said my delay was only between 15-29 minutes. I contested this and they rejected it. My only recourse was to submit a formal complaint to which I've yet to receive either a reply or acknowledgement that it's been relieved.
As far as I'm concerned they're a bunch of money grabbing crooks who treat their fare paying passengers like $h!t.
You should contact LondonTravelwatch and raise a complaint through them