Flags and banners were decorative pieces containing symbols that was used to represent a government, group or individual. Typically these pieces were used to represent patriotism or ownership.
The flag of the United Kingdom was the Union Flag.
Plain white flags were normally used in the event of a surrender. The Doctor, holding a sheet of A4 paper on a stick, met a group of Cybermen, jokingly apologising for not having an actual white flag. (DW: Doomsday)
The Threllip Empire flag was grey. (BFA: Living Legend)