As I recall the cork tip was just that, not a filter, a thin layer of cork round the tip to stop the paper getting wet and soggy, filters came later.
My dad smoked about forty a day Woodbines when he was working in the factory during the war and doing nights in the Civil Defence but gave up abruptly when he was in his forties and never smoked again.
Mom continued smoking until her death but only about ten a week Park Drive................Dad used to say "Filthy habit.! so she went to the loo for her fag.