Outrageous... you may be able to file a claim in small claims in the UK online, you do not have to appear in person in court. I am attaching a link
https://www.moneyclaim.gov.uk/web/mcol/welcome
I am not 100% sure if people residing abroad can use this service, read through the link carefully before filing. I have used this service and it is very good, simple and straightforward and is completed entirely online. Before you file, you must send a letter to BA outlining your grievance, what you seek as a remedy and put a reasonable deadline to resolve the issue (30 or 45 days). In the letter state that you will be filing a claim in the Small Claims Court on XXX date, if BA have not responded by this deadline. Then do it... BA know they have failed miserably to address the problems at LHR. 300,000 passengers were affected on BA alone. This is why they cannot devote time to tracking individual bags...the truth is they are relying on the airports to "repatriate" the luggage to LHR and they will then forward it. That is not acceptable and they are failing in their duty to resolve the problem.
As is often the case, the airlines seek to defend their actions as the result of "exceptional" weather. The weather was exceptional, but that is not what the problem is. The problem is the utter lack of responsiveness of the airline subsequently and their total failure to communicate. The massive staff cuts that the major airlines have made in staff have serious repercussions when things go wrong, as they simply do not have the resources to fix the problems. The same happened following the huge storm in the North East last week. Airlines need re-regulating... deregulation has simply not worked.