Whilst I appreciate that many of the replies here are given in good faith, I am rather disturbed that the implication is that, assuming all the facts supplied are true, the Penalty Fare would appear unfair but that it is more trouble than it is worth to appeal it.
As this response is presumably informed by my own advice as much as anyone else's, perhaps a reply is in order.
I did make a big assumption - that the OP has plenty other things in life to be getting concerned with, and while accepting a solution to pay-and-forget may leave a lasting sense of injustice, I was contrasting that with the experience of several others who have been consumed for days or weeks, and in some cases months, by anxiety, hope and anticipation, with little more than their own thoughts to console them while they wait for a letter, and then another, before reaching an outcome. For the cost of a meal out, I assumed that the latter just "
wasn't worth it".
I base my experience on, among other things, having assisted others in fares disputes, several with FCC. While those outcomes have been favourable, it has been clear to me from regular emails and texts (e.g. "I didn't get a letter today, what should I do?") that these are very stressful experiences. Some people have complained of sleeplessness. If there was also a detrimental effect on their personal or work lives, I don't know. Now admittedly, most of these have been whan passengers are faced with outcomes that include prosecution, and that isn't a possibility here (apparently), but the same balances of cost vs. time and of assurance vs. doubt applies.
All this is in stark contrast to those regular posters on here who are likely to have a much easier time working with the industry, perhaps do work in the industry, and for whom the whole matter is mundane and 'just another job'.
My assumption about the OP may have been wrong. Perhaps the cost of a good meal out is worth the letters, phone calls and the waiting. I hope I left that option wide open and proposed firstly settling the Claim, and then making their own choice "to take a punt" on writing a letter, complete with suggestions on what to include and to exclude. I hope they were able to make that decision based on the advice.
It's not like you,
thedbdiboy, not to read posts carefully, so either in this one instance you have rather skimmed my advice and the comments from others, or else I have been unclear; in which case, I hope this further clarifies my assessment.
I'm aware of the advice to staff to be more vigilant in applying discretion during the
London 2012 period, but the facts of the matter is that the OP and their fellow travellers are where they are: wronged but with little or no evidence, and FCC are where they are, with a huge amount of appeals and investigations by officers who have no first hand experience of the incidents they are investigating.
My assessment is unchanged, but thanks for giving me the opportunity to expand on my advice. If the OP is still with us, then perhaps this will assist them in reaching their decision in which course of action to take.
Just because XC do not accept Groupsave on their trains does not mean they cannot issue them for onward travel on a different operator. The relevant fares are in the Avantix machine. 
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