What are my chances in court to have this thrown out?

Hi All, This might be lengthy so I apologise. I'll start of by explaining my journey and what I've done since and hopefully see what advice there is. I'm feeling bullied and treated like a criminal for what ammounts to a mistake i rectified as soon as possible. I took an early train from London st pancras to london gatwick (airport) at around 3:30am Tapped in with oyster card at st pancras Got to the other end and asked the staff where to tap out - got taken to a inspector and told I had to pay a penalty as I was 1 stop outside the oyster zone. I explained I couldn't pay the £20 and I had a flight to catch and couldn't he just sell me a ticket from the last stop. He said that's what he was saying and I could simply pay the minimum £5 single fare and deal with the rest on appeal. Took my penalty slip, caught my flight, thought nothing more of it, got back a few days later and due to my accommodation (hostel) I managed to misplace most of my paper work, which meant re-printing flights etc but thats a seperate matter. Unfortunately I didn't have the fare letter. Fast forward to a few weeks ago and I now have a 'Final Notice' that I avoided my fare and had admin costs etc to pay. I wrote back, explaining the situation that I believed I was going to a london station, paid the remainder of my journey on arrival and had no chance to do otherwise. I'm now facing a 'Notification of Alleged Fare Evasion' and a fee to pay of £55 (£20 fare, £40 prosecution, -£5 already paid) The letter states 'I therefore contend that the intention of crystalgeek was to travel on the railway without having previously paid and intent to avoid paying' which is completely untrue - the ticket inspector checked my oyster card and saw I had tapped in. What do I do now? Will I have to go to court and if yes, what chance do I have to prove I was travelling without having payed and intending not to pay The letter quotes Section 5.3a of the Regulation of Railways Act