Obviously keep your boarding pass and any proof that you arrived before the time (e.g. a photo of the ARN screen with the time showing on it). You have two approaches: a customer service based remedy based on Customer Services, and Involuntary Denied Boarding, if you believe you complied with the instructions for boarding. You may want to try the first approach first and fallback to IDB if that fails, a separate team handles that. The main 261 Regulation thread will give more information on the latter. However on IDB BA tend to be particularly loathed to pay up, hence why I suggest it that way around.