From what you have posted so far I'm struggling to find any obvious routes of challenge that would provide a decent chance of success.
Motorists must be allowed a 'consideration period' to consider the terms and conditions on offer and either decide to accept them and park, or to decline them and leave. Whilst the BPA specifies a minimum period of 5 minutes, the IPC, of which Excel are a member, do not specify, simply saying it must be 'sufficient'. Not only was the drivers stay a lot longer than 5 minutes, by your account of the situation they didn't use the time to consider the terms, instead taking a phone call.
With this in mind, it may be worth considering paying the discounted amount. There's no harm in speaking to Iceland to see if they'll help, but if the driver was not a customer they're probably unlikely to.
Just to check there aren't any other options, do you have and photos of the signage?
