Product: Credit card or prepaid card

Barclays credit card won't retrieve a refund for unprovided services. All details attached. 

Barclays bank credit card ( mastercard ) gave up on retrieving a disputed amount of {$1.00}, XXXX. XXXX from a travel agency called XXXX. Please see their final letter attached. Barclays bank is now asking me to repay all that amount, I believe I shouldnt have to pay that money, XXXX should send the refund of the money because they didnt use the money for what I paid for, as explained below. I have attached all relevant documents I have. 
On Friday XX/XX/, I urgently purchased a plane ticket for my daughter, XXXX XXXX from XXXX, XXXX XXXX to XXXX, urgently because the XXXX XXXX XXXX asked me to expedite the process to meet the criteria for her situation. In this case, I unintentionally paid twice with Barclays credit card around the same time to two different travel agencies, XXXX, and XXXX. Only one of the payments was received by the airline from XXXX, per airline representative. Now Im fighting to retrieve the other payment from XXXX  but they keep rejecting my call and Barclays wont help either. How did this happen, all explained below. 
I made my first payment to XXXX XXXX through XXXX XXXX, and they gave me the booking # XXXX, ticket # XXXX ( also confirmed later by XXXX XXXX, XXXX  XX/XX/ ). ( Please see attached print-out proof of payment, and if necessary, you can also confirm that with XXXX XXXXXXXX ) XXXX Some hours later after my first payment on the same dayXX/XX/XXXX, I called the same number to confirm whether the transaction had been processed successfully. This second call unfortunately, happened to be picked up by XXXX. I didnt know that this agent talking to me was from a different company. I asked him to check the status of my purchase, I gave him all my information he checked the system and said to me that it didnt process and that he can help me get a plane ticket for my daughter. 
I asked him if its not going to be a problem of double payment, he said not at all. Then I paid XXXX to him, name XXXX per his request. He sent me a booking # XXXX. ( Please see attached booking and payment ). He assured me that he will send the plane ticket after its been generated by the airline. Few days later, I saw on my account XXXX pending payments. XXXX XXXX representative said to me that the payment was done by XXXX XXXX, no record of XXXX. Although the XXXX cancellation window was over ( while waiting for the ticket # from them ) at that time, I still tried to reach XXXX but each time we start talking about what happened, I get disconnected ( they hung up on me ). 
I called Barclays bank to dispute the charges, after several back-and-forth discussion about the issue, they said I must write a formal letter to dispute the charge. Barclays bank, also decided to send me a new replacement card to avoid or mitigate any fraud. That is why the attached receipt shows the previous credit card instead of the current card number. On XX/XX/ I wrote a letter to Barclays bank XXXX department to file a dispute. During my follow up calls to the bank, they assured me that they will do everything in their power to retrieve the money back but on XX/XX/, I received a letter datedXX/XX/XXXX from the bank stating that they couldnt help me with this matter, adding that the XXXX will remain on my credit balance to pay back the money to them. On Monday XX/XX/, I called the bank and talked to XXXX XXXX, he reinstated that I am responsible for the money because of insufficient proof of contract and cancellation. 
During our phone conversation with XXXX, I asked if I did anything wrong by paying before service, he said, No. I added that for all online transactions, everybody pays first before service. If the product is not received or if the service is not provided, then a refund must be made. I said this is the expected role of the bank to make sure that the refund is processed back to their clients account. I added that I XXXX for XXXX made a payment, let him provide a proof/receipt of payment to XXXX XXXX XXXX XXXX XXXX agreed with me on that explanation and my expectation from them, but he still says I must pay the money back. Before the end of our phone conversation, I requested him to send me my bill of rights indicating where to file a report, and he promised to do so. At this time as XXXX writing, indeed, the money currently reflects on my XXXX account, XXXX XXXX failed to supply the information I need for my next step. I XXXX around and discovered that you can help in this situation. I need your help in this matter, please, please, please, because XXXX cant XXXX how long it will take me to repay all this additional {$1800.00} plus interest. I already owe them over {$10000.00}. Please help me. You are my only remaining hope to rescue me. XXXX XXXX bless you at your job, everyday.