she is 30!!! It happened at Liverpool Street. She has had a really bad year and this just tops it of!

My sister has used a child ticket (she is a adult !) She did not start the journey as the ticket enforcer stopped her as she passed the barrier. He questioned her and said that she needs to be honest or it will get worse. He asked her if she had done this before and she admitted twice. He said he was sending the paperwork to his office and that they will check CCTV, is this true? He also believed that she was going to travel further. He then let her get on the train without any ticket? She is totally remorseful and would like to avoid court proceedings. Is it worth her contacting National Rail now with a extreamly appologetic letter and asking to pay and administration Fee to cover the costs? Many thanks for any advice.