HB, that applies to penalty fares, where the penalty is the higher of £20 or twice the single fare, so although it involves the “peak vs. Off-peak” issue, I’m not sure it applies to the OP’s situation.
As many as 10,000 rail travellers have been overcharged after being caught and penalised for not having a valid ticket.
The Rail Delivery Group (RDG), the industry body that represents private train operators as well as Network Rail, has admitted that tickets inspectors have overcharged fare-dodgers to the tune of tens of thousands of pounds after rail companies failed to implement a rule change introduced in April 2018.
I'm about to post this in a new thread, don't know if it affects you but there are quite a few rail companies involved.
OP has had their refund offered already : suggest you re-read OP’s posts for confirmation, although they didn’t get it because they were then asked to leave the station for saying the refund alone wasn’t enough (the OP’s version of events).
You can bet the gateline staff’s version of events will be along the lines of “refund offered in an attempt to de-escalate the situation, but despite this situation escalated requiring security to be called, and the passenger was escorted from the station”.
It’ll be a “he said, she said”, and I can’t see a complaint going far. It doesn’t matter if a ticket has been paid for or not : once it gets to the stage where the staff deem behaviour sufficient for the passenger to be denied use of the station they are entitled to refuse travel, and unless the OP can show this was entirely unreasonable the OP is on shaky ground.
Demanding “more than a refund” from the gateline staff will make it hard for the OP to show they were being unreasonable, especially if the gateline staff’s version of events mentions this and even hints at any concern for their safety: how do you imagine they’ll have written it up?
Don't touch them owe me £500 since January 2019 make excuse after excuse. Seem they always have software problems sending money out. Keep saying they will call back or email nothing been chasing it now for 6 mths the phone staff always have the same banter we will chase it up and get back to you then nothing!