What's that red thingy that UK politicos wear on their lapel?

The remembrance poppy (a Papaver rhoeas) has been used since 1920 to commemorate soldiers who have died in war. They were first used in the United States to commemorate soldiers who died in World War I (1914–1918). Today, they are mainly used in current and former Commonwealth states to commemorate their servicemen and women who have been killed since 1914. In those states, small artificial poppies are often worn on clothing on Remembrance Day/Armistice Day (11 November) and in the weeks before it. Poppy wreaths are also often laid at war memorials.

http://en.wikipedia.org/wiki/Poppy_appeal

It's a representation of a poppy, in remembrance of those who died in the poppy fields of Flanders - you are quite right, and better informed than many.

11.11.11 is the 11th. Hour of the 11th. Day of the 11th. Month when the end of war was declared.

It's a poppy worn the few weeks before/up until Remembrance Day. It's worn in Canada too, to Remember 11.11.11. Not sure where else it's recognized. It's a nice gesture.

It would be a poppy, and it represents veterans. It's sad that it isn't part of the American Veteran's Day ceremonies.