Clearly, for some reason, the bus provision on the occasion of the OP's trip was insufficient, but seemingly there is no obligation to deal with passengers whose journeys are disrupted as a result?
They are obliged to deal with them, either by accommodation on the next service or otherwise in line with the PRO as explained to thread. They are not obliged to fetch taxis or spot buses for people who have not suffered severe disruption (that is, an hour or less) just because they are going to an airport or birthday party or driving test or whatever.
The passenger can try to leverage their statutory rights by claiming the service was not provided with reasonable care and skill but there is no guarantee of success. The fact a bus was full is not evidence of that alone - the provision has to be in line with expected industry standards and so on. The result and impact on the passenger are basically immaterial to that test, but the actions and mindfulness of the service provider are material. If XC say "this is in line with the usual passenger loading for this line (presents data) and we adhere to the industry standard" that is a fairly good defence.
Of course we hope they get their refund, but also this sort of trip planning where they left no redundancy in the event of a mishap and now must rely on asking for £75 back is asking for trouble. There are frequent NX buses to Stansted from Cambridge which are reservation only and are far more reliable.
