The Union Flag was the flag of the United Kingdom.
Name
Rose Tyler corrected Eddie Connolly's mistake of calling it the Union Jack, which is a name used only when it was flown at sea. She also corrected his positioning of the flag when he had hung it upside down. (DW: The Idiot's Lantern)
Recognition
The Union Flag was primarily used to identify the UK. The Prime Minister of the United Kingdom would sit between two Union Flags while addressing the nation. (DW: The Christmas Invasion)
Ironside Daleks had an image of the Union Flag in place of their recognition code. This identified them as British soldiers. (DW: Victory of the Daleks)
The Union Flag was often flown atop of government buildings to identify them as such. (DW: The Christmas Invasion)
As late as 2493, the Union Flag was used as recognition for spacecraft that were property of the United Kingdom. An example of this was UK-201, which bore the flag on its hull. (DW: The Rescue)
Decoration
The Union Flag was also used in a decorative manner. Rose Tyler wore a shirt with the flag on while visiting wartime England. She noticed the irony of it when she found herself facing a bombing raid. (DW: The Empty Child/The Doctor Dances) The Union Flag was also flown from a flagpole in some places, for example, in the entryway to Farringham School for Boys. (TW: Human Nature)
In 1941, The Ritz was decorated with numerous Union Flags (TW: Captain Jack Harkness) and during World War II, people often decorated streets and bomb shelters with it. (DW: The Empty Child)