I recommend you to make a second stage appeal following rejection of your initial appeal. The second stage appeal can be on the same grounds as those of the first.
Any challenge to an appellant's assertion as to the station at which boarding took place is one in respect of which it is up to the operator to “provide evidence that reasonably demonstrates that” such assertion “is not true” (Railways (Penalty Fares) Regulations 2018 Regulation 16(4)). As there has been no challenge to your statement that you told the collector that boarding took place at Hinckley, not Nuneaton, the appeal should be determined on the basis that boarding did take place at Hinckley. That reinforces the point that the penalty fare was for an incorrect amount, having been based upon a full single fare from Nuneaton (£13.70) rather than from Hinckley (£9.70), and, being an excessive fare for the Hinckley-New Street journey, was one not charged in accordance with the Regulations' requirements. Your further grounds of appeal should draw attention to the difference between the fare from Nuneaton and the fare from Hinckley by detailing the amount of both and pointing out the overcharge.
I note that there have been a number of failures on the part of the appeals body to observe the appeals procedure requirements set out in Schedule 2 to the 2018 Regulations. In relation to this Regulation 16 appeal the appeals body has failed to state that a further appeal would be considered by a different person (Para. 8(b)) or that if such further appeal failed the appellant would have a right of appeal to a Final Appeal Panel (Para. 8(c)). Nor has the Appeal Panel given reasons for its decision as required by Para.7(c), thereby depriving the appellant of any basis for understanding why the appeal has failed.
The argument that signage at Hinckley, the boarding station, was non-compliant due to the absence from it of the Cross Country logo/name is attractive but may be ineffective due to the stipulation in Parargraph 2(2) in Schedule 1 to the Regulations: “The absence of a logo or name, as required by sub-paragraph (1)(f), on a notice only invalidates the notice in relation to the operator whose logo or name is missing.” (my emphasis). It might be fatal to any PFN issued by XC, but the PFN here was issued by a WMT collector purporting to act on behalf of a station operator rather than by XC's collector. The East Midlands Railway website lists “EM” as the only “Applicable Operator” for penalty fares purposes, so possibly the absence instead of WMT's name or logo from any PF signage at Hinckley opens the way to an appeal that the PF should not have been charged on the ground that “the requirements for the display of notices specified in regulation 8 were not satisfied” “at the station where the passenger boarded the train” (Railways (Penalty Fares) Regulations 2018 Regulation 6(2)).