I cannot afford to pay £1200 plus fees and a fine if I'm found guilty of something that I didn't do.
I think you could have done with specifying all this information up front.
In terms of sleeping well at night, I think one thing you may have overlooked in all this is if you accept responsibility for what this person has done what impact it may have on you going forwards. I think you need to know what you are being prosecuted for and get advice specifically on that, as some types of prosecution are more serious.
Also, you have another thread where you travelled past your ticket validity. If you accept responsibility for someone else's wrongdoing, what if it means subsequent misdemeanours actually by you might be treated differently, perhaps less leniently?
And lastly, if you accept responsibility, what is to say that this can't happen again or to an even greater extent? Might your accepting responsibility for this possibly complicate your ability to show that you have nothing to do with such matters?
You started this thread with a very short term view of "how much should I budget", when in fact I think the first thing you needed to do was find out what the chances of actually defending your good name are and how you might go about doing that. If I were in your shoes that is what I would do, and whilst I may have asked a legal secretary friend for their opinion I wouldn't be treating it as definitive but seeking full advice.
I don't think you have any basis to believe they are convinced they have enough evidence when (on the basis of what you describe) all they have so far is your silence. If you picture the process on their part, they will probably have written and written and written, and been "ignored", so automatically moved to prosecution and just won by default because you were unaware. I feel it bears no relevance as to whether you are or are not able to defend on the basis that you say this was not you, now that you are aware.
The point made about the photographic evidence is right. You have sought it you say, but you also say they won't provide it - so what have they got? Also, another matter for you to check out is if the position stated (about needing permission from everyone in the footage) is even correct or not. I can't advise you on any of this, other than to advise you to get advice rather than just deciding a course of action without knowing all the facts and options open to you.