First of all, the general rule of thumb is the same: you have a chance to get Mafia Wars British passport by doing jobs, fighting or robbing. The more you do it, the bigger the chances to get the items.
Last time, I noticed that the New York jobs used to give us the most Parisian Maps and I tend to believe that the same will happen with the London Challenge, so make sure you try doing Consigliere and Underboss tier jobs to maximize the amount of British Passports you get. If that doesn’t work, Cuba and the first tier of missions will certainly get your pockets filled with passports.
Where did you find the most of your British Passport loot?