Hi, it sounds like you weren't fined, but issued a Penalty Fare. This may seem like a fine, but it's actually a fare charged at a higher than normal rate that allows for disposal of certain minor ticketing infringements without the need for prosecution. I'd say that provided they're satisfied that was it and you've paid the penalty fare you're fairly safe. They may however look into other occaisions of this oyster card being used. To clarify, was this an Oyster containing a season ticket or discount? Or was it a Pay as you Go Oyster?
They seized the Oyster card as it had been misused and to prevent it from being used again.
If however you've been making many journeys using said Oyser and it contained a discount or season ticket, you could potentially be in trouble, but it would be for them to prove that it was you using the Oyster. How did you answer any quesitons? They can't send you an 'extra fine', as only a court can impose a fine, they could however investigate further and bring prosecution proceedings, others will advise on the likelihood of this and whether they've limited their options by charging the penalty fare. However, as you've paid the penalty fare, I'd say you've discharged your liability for this particular journey.
Also, who are 'they'? Transport for London or a private company? I'm guessing the former. Did they take any witness statements (eg. an MG11), or just issue the penalty fare? Were you interviewed under caution?
You need to wait about seven months to be sure you're in the clear. Why seven months? They have six months to lay papers before the courts and sometimes if they lay papers last minute there can be a delay in the court contacting you.
I'd say it's likely to be 'case closed' if they've issued a penalty fare, if they were planning on investigating further you'd typically have been reported for prosecution and not have been given instructions to pay anything until investigations were completed (note: TfL don't generally do out of court settlements). But this is not 100% guaranteed.
I'd also like to say that in the case it was just a penalty fare and that's that, don't do it again thinking the risk is worth it. You'll likely face a court case if there is to be a next time.
