The problem I see with this is that I can't see any business being prepared to agree an anonymous free pass. In the first place, I imagine whoever received it would feel doubtful about it, and if then asked to rationalise the doubt they would probably say something like 'without knowing who is involved, how do we know that the £1,000 offered isn't to stop us pursuing losses of £10,000?'
It seems to me that if the OP wants to try to come to some sort of agreement with the railway, then they'd need to go through a solicitor in that the railway might be prepared to agree if they knew that the solicitor meant that there was some way to contact their otherwise anonymous funder. But even then I would emphasise that this might work rather than it certainly would. And as people have commented, if a solicitor was prepared to do this, they would charge handsomely for it.
So realistically we are unable to suggest a way out of this that will guarantee immunity from prosecution.
In that light, the OP has to consider which of the remaining options will be best for them after taking everything into consideration:
- keep quiet, and hang on to the money. This will feel like not taking responsibility - but should the railway ultimately catch up with the OP, they will have the money to hand to resolve the matter in court
- make a donation to a suitable charity (it might be worth having a look at
https://www.thameslinkrailway.com/about-us/corporate-and-social-responsibility/charities to see who Thameslink corporately support) which will allow the OP to take responsibility, but won't prevent court action if GTR ultimately go down that road.
Neither of these routes are perfect: the decision to make is what points to compromise on.