Falsely Accused of Theft

My friend and I were accused of theft and banned from a large supermarket near our homes. The security guard yelled at us while the assistant manager watched him and reiterated the same. We were publicly humiliated. This is what we did. We each got a pie with a reduced label on it and put them in our trolleys. We continued shopping. We saw a store employee giving items final markdowns. About 10 people were handing her things from their trolleys to get marked down. We did the same. My friend handed both pies to the store assistant who duly marked them down. Shortly afterwards we went to the checkouts and paid for them. Subsequently, we were called over by the security guard and assistant manager. The guard yelled that we had the pies in our trolleys for some time before getting final markdowns. He said if we had not done this there was a chance someone might have purchased them at the higher price. He said this meant it was theft and we were banned. They did not accuse us of not paying for them nor did they look at our receipts or the items. We are regular shoppers who get all our groceries in that store and sometimes mark down items. We know lots of staff and customers. Some staff came outside and expressed shock. Our repuations are tarnished. I wrote to head office explaining in detail what happened and asked for an apology and for the ban to be lifted. No response. We are more concerned about our repuations than anything. Their definition of theft is unacceptable and surely unlawful. If they don't want shoppers to put things in their trolleys and get them marked down they should not allow staff to mark down such items. Around 10 or more people did the same but were not humiliated or banned. Any advice would be much appreciated.