Flags and banners were decorative pieces containing symbols that were used to represent a government, group or individual. Typically these pieces were used to represent patriotism or ownership.
Plain white flags were normally used in the event of a surrender. The Tenth Doctor, holding a sheet of A4 paper on a stick, met a group of Cybermen, jokingly apologising for not having an actual white flag. (TV: Doomsday)
The Threllip Empire flag was grey. (AUDIO: Living Legend) The Tragellan Empire flag was red. (COMIC: Beneath the Skin) The Karturan Congruity used a holographic flag. (AUDIO: The Forever Trap) The Women's Institute had a flag with a crest. (PROSE: I Am a Dalek)