However, by saying they went to the ticket office at Brighton, the OP has admitted they had the opportunity to buy a ticket before they boarded the train from Brighton. The penalty fare people might say it was an unreasonable wait at Brighton, but there is nothing in the FRPP about that and it is still the OP's responsibility to purchase the ticket before travelling.
Under the Ticketing Standards Agreement, passengers should not expect to wait more than five minutes for a ticket at peak times, three minutes elsewhere. I'm not blaming the RPI's for not knowing this, as there's no reason they should, but that agreement is there for this sort of case.
However, I'll admit to having misread the post earlier - I didn't notice the Portslade to Brighton part. This is key, because the NCoC states that:
"you will be liable to pay the full single fare or full return fare or, if appropriate, a Penalty Fare (see Condition 4) for your journey. You will not be entitled to any discounts or special terms unless either:
(i) at the station where you started your journey:
* there was no ticket office or no ticket office was open and
* there were no self- service ticket machines or no self-service ticket
machines were in full working order and
* in Penalty Fares areas you bought a Permit to Travel unless no Permit to Travel issuing machine was in full working order:"
It's clear here that the regulations apply to the point at which you've started your journey, which is Portslade. If you didn't attempt to buy a ticket here, or leave adequate time for the ticket, then I don't see that you'd get any success in this.
As for the excesses at Vic/London Bridge - these should be there for passengers who have met all of the 'unless' criteria which are listed in the NCoC.