During World War I, the cartoonist Bruce Bairnsfather created a popular character called 'Old Bill'. He was a grumbling veteran soldier with a large moustache. In the 1930s - perhaps because many ex-soldiers had become policemen - the name became attached to the Metropolitan Police. It has to be said that the Metropolitan Police themselves have a website that offers a variety of other possible explanations. If they don't know for sure...who does?