I suggest you address the following points in your reply to TfL:
- That you are sorry for what has happened
- What you have learned from the incident
- That you are keen to settle the matter without the need for court action
- Offer to pay TfL's administrative costs in dealing with the matter
It's probably also worth pointing out in your reply that the you were allowed to touch in before continuing your journey so technically you have paid for your journey.
TfL are less forgiving than their National Rail counterparts and often prosecute under the TfL Bylaws. Also, they don't normally offer out of court settlements although they have been known to give a final warning in certain circumstances.
Feel free to post a draft copy of your reply in this thread and forum members will be happy to proof read it for you.