If you were denied boarding without reasonable cause, you are due compensation for that under EC 261/2004. This is a much broader provision than the US provides.
However, whether you succeed will depend on why TP cancelled your tickets. It seems a bit odd to do so given that the chargeback was denied, but then again disputing legitimate charges is always risky.
I suspect that you will need to file a claim under the Regulation, have it denied and pursue it through small claims (which, if you use the UK system permits telephonic hearings).
For the benefit of others, Amex US generally permits chargebacks for up to a year, even though US law only requires 60 days. Never initiate a chargeback until after the travel is completed. Nothing good comes of it. In addition, if the fees were not refundable, what is the basis for the chargeback. An increasing number of merchant vendors react "poorly" to such chargeback attempts as they are expensive and disruptive.