Refuse to take responsibility for faulty product

I discovered a cigarette with a faulty filter in 3 seperate packs of Dunhill Lights, on 3 seperate occassions over several months. I emailed BAT customer care to complain about the issue. I only contacted customer care on 2 of the 3 occassions however. The first time I called I didn't ask for compensation for cost or inconvenience. I only hoped that BAT would take greater care to ensure their quality checking processes were more stringent from then on. I was however told that if I wanted compensation I would need to hold on to the cigarette as proof of fault. I could not submit a pic. No mention of anything else. After finding a third cigarette with a faulty filter I had had enough and asked for compensation. I took a pic as before and kept the cigarette as advised, only to be told this time that I also needed to keep the box! You are refusing to take responsibility for a faulty product and compensate me for the purchase of a PREMIUM product which should be perfect in terms of quality.