Without the requested information, I can only provide you with some general information on this topic. Hopefully, it will still be useful to you. First of all, I am sorry to hear about the issues brought up by this. It must be a frustrating situation to be going through.
If you cannot get the airline to pay you the money as promised and your card provider also cannot help, your only option will be to consider legal action to try and get the money that way.
If money is owed by one party to another, the debtor can potentially be taken to court to try and force them to pay up. However, as legal action should only be used as a last resort, there are certain steps that should be taken initially to try and resolve this matter informally and without the need to involve the courts. It is therefore recommended that the following steps are taken in order to try and resolve this:
1. Reminder letter – if no informal reminders have been sent yet, one should be sent first to allow the other party to voluntarily settle this matter.
2. Letter before action – if informal reminders have been sent but have been ignored, the other party must be sent a formal ‘letter before action’ asking them to resolve this amicably within a specified period of time – 14 days is reasonable. They should be advised that if they fail to make contact to resolve this matter, formal legal proceedings will be commenced to pursue them for the money that is owed. This letter serves as a ‘final warning’ and gives the other side the opportunity to resolve this without the need for legal action. There are numerous templates available online for such letters and a simple search will bring up a list of useful results.
3. If the letter before action is also ignored, formal legal proceedings can be initiated. A claim can be commenced online by going to https://www.moneyclaim.gov.uk/web/mcol/welcome. There will be a fee payable, which depends on the amount that is claimed. The debtor will eventually get a copy of the claim and they will have a limited time to answer it. They could accept it and pay what is owed, they could accept it only in part and defend the rest, or they could outright reject it. They could also completely ignore it, in which case judgment will eventually be entered automatically against them. Also, it is worth noting that the simple act of submitting a claim could show the debtor that this is being taken seriously and prompt them to consider negotiating a potential solution to stop the claim progressing further, such as offering full or partial repayment.