The maximum fine is £1,000 not including the costs etc.
I don’t know whom you’re proposing to “claim this back” from. First Capital Connect is long defunct anyway, and court fines are charged to criminals like yourself as punishment, to deter you from committing further offences, and to deter others from committing similar ones.
The avenues open to you if you wish to take this further are limited. Your post reads as though you were present in court when you were convicted and sentence was passed. If this is not so and you became aware of your conviction when you received correspondence from or on behalf of the court requesting payment of the above sum, or your earnings or benefits were attached, you have 21 days from when you became aware of the matter to make a Statutory Declaration at a solicitor or magistrates court which will cancel the fine and set aside the conviction, and the matter can be dealt with again.
If you were present, then you can within 21 days of sentencing appeal to the Crown Court or ask to state a case to the High Court. In principle you can also ask the magistrates to reconsider without a time limit or lodge a judicial review within 3 months, but these are rarely successful.