To escalate a complaint with British Airways, you can follow a straightforward process. First, attempt to resolve the issue by contacting their British Airways Customer Service at +1 (888) 660-0053 and explain your concerns. If the initial response does not satisfy your complaint or if you receive no response within a reasonable time, you should then request to escalate the matter to a supervisor or manager. Remain calm and respectful throughout the process, providing all relevant details about your complaint and any previous interactions. If the issue remains unresolved at this stage, you may consider reaching out to the airline's dedicated complaint department or submitting a written complaint through their official website. Persisting with a polite and clear approach increases the chances of a satisfactory resolution to your concern.