Carefully read everything you have received. Fines are partly set in accordance with known income and if that info isn't provided, they have to assume you are on top whack. It's also easy to assume that instructions ignored = indifference, when it may be somebody swamped with the legal paperwork.
The posts above already include advice about this. I'd recommend paying attention to
daveg. He's a serving magistrate so he knows the type of thing going through their minds. In this context, he mentions the apparent absence of the offer of a fixed penalty, rather than a report for summons. If the reason isn't clear in the police statements, make the point - in a polite way - that you were not offered the benefit of the chance to pay a fixed penalty.
It can be daunting attending court and it's generally time consuming but a polite apology in person cannot do any harm (again see
daveg above.) Bear in mind that lay magistrates deal with endless lists of 'guilty by post' and 'proved in absence' cases.
On the subject of mitigation: There are a couple of different ways cases are dealt with but if you receive papers offering the chance to plead guilty by post, there will also be space for your mitigation. If you put anything which means "I'll plead guilty but I didn't do it" they should adjourn the case and offer you the opportunity to plead NOT GUILTY. The will only accept an unequivocal GUILTY plea. If your mitigation is "I committed the offence by crossing the STOP line, but the prosecution evidence does not make clear that I waited just beyond that line until it was safe to continue" that would be accepted because you are admitting the offence (although I've no idea how your explanation might be received.)
I'm not up-to-date with fines, but whenever I see any reports, the fines imposed on cyclists seem harsh. The one that sticks in my mind was a cyclist in Brighton on one of those police reality type programmes. He was riding along the pavment in the dark without lights and eventually passed a red light, although he did wait at the actual junction. IIRC, the total bill was something like £750.
viewtopic.php?f=15&t=43040My comments are based on being a fairly experienced prosecutor, but without recent experience. I've found it virtually impossible to check the current position because google just brings up ads from solicitors eager to drum up business.