A good lawyer will always advise a client who faces a claim for money to "try it on" and come up with some BS excuse. In many cases, the person making the claim will give up and go away, particularly when it's from a non-lawyer who is claiming no more than a few hundred pounds. When you buy a ticket from an airline, the contract is with the airline - you have no contract with the airport or handling agent and if you write to the airport or handling agent, they wil (correctly) refer you to the airline.
You will likely have to write to the airline maybe 2 or 3 times, refuting any BS excuses, and possibly threatening court. Eventually the airline may back down and pay money for your claim.