The British Army was a branch of the United Kingdom's military. The Doctor worked directly with them on occasion; he was also involved with them through UNIT.
History
18th century
In 1746, British troops, also known as "Redcoats", fought against the Jacobites in the Battle of Culloden. (TV: The Highlanders)
19th century
In the early 19th century, the British fought against Napoleon in the Napoleonic Wars. Under the Duke of Wellington, the British defeated the French at the Battle of Waterloo on 18 June 1815. (PROSE: World Game)
During the First Afghan War, the British Army was afflicted by poor planning and leadership, leading to huge disasters such as the retreat from Kabul in 1842. A new British army invaded Afghanistan later that year, ending the war, (PROSE: Mire and Clay) although the British Empire became involved in further engagements in Afghanistan in later years. (PROSE: All-Consuming Fire)
From 1853 to 1856, the British, with French and Turkish allies, fought against the Russians in the Crimean War. (TV: The Evil of the Daleks) A miscommunication on 25 October 1854 led to the infamous Charge of the Light Brigade, where a light British cavalry brigade was sent to advance upon the wrong Russia positions and were slaughtered. Florence Nightingale arrived at the Scutari barracks on 18 November 1854 and helped clean up the medical institutions to provide better aid for the sick and wounded soldiers. (AUDIO: The Angel of Scutari)
After the end of the Indian Mutiny in 1857, the British Army was sent into India to maintain order. (PROSE: All-Consuming Fire)
20th century
From 1914 to 1918, Britain and its allies fought World War I against Germany and the Central Powers. Some of the battles the British were involved in included Passchendaele, the Somme, Gallipoli, Verdun and Ypres. (TV: The Sea Devils, To the Last Man, AUDIO: The Next Life, PROSE: Byzantium!, Remembrance of the Daleks, Illegal Alien) A million British soldiers died during the war. (TV: To the Last Man)
In World War I, several British troops, also called "Tommies", were abducted by the War Lords for their War Games. They helped the Second Doctor and his friends defeat the War Lords. The surviving troops were sent by the Time Lords to their right time zone. (TV: The War Games)
At a different point in World War I, the New Dalek Paradigm interfered in the course of the war by influencing British and German industrialists to manufacture robotic, Dalek-like drones, supposedly to assist members of the British and German armies, respectively. However, their true plan was to use the Proto-Daleks to wipe out the British and German soldiers who were aware of their existence, in order to eliminate all evidence of their interference. (COMIC: The Dalek Project)
From 1939 to 1945, Britain and its allies fought World War II against Nazi Germany and Japan. (PROSE: Timewyrm: Exodus, Magic of the Angels; AUDIO: Casualties of War; COMIC: Sky Jacks)
Tommies being exterminated by a Dalek. (TV: Victory of the Daleks)
In 1941, two British soldiers who came to protect Winston Churchill were exterminated by the Daleks. (TV: Victory of the Daleks)
When WOTAN tried to conquer Earth on 20 July 1966, the British Army fought against its War Machines. (TV: The War Machines)
Some time before the formation of UNIT, a squad of British Troops led by Colonel Alistair Gordon Lethbridge-Stewart (who later founded UNIT) fought against the Great Intelligence and its Robot Yeti servants. (TV: The Web of Fear)
Following the formation of UNIT, the British Army — often referred to by the organisation's personnel as "the Regular Army" — appointed a UNIT liaison officer to whom the officer in charge of the British branch of UNIT reported. At the time of the Auton incident, Major General Scobie was the British Army's UNIT liaison officer. UNIT troops were usually members of the British Army serving on detached duty, and were thus subject to the orders of British Army officers. (TV: Spearhead from Space)
During the time of Mars Probe 7, the army had a new Space Security Department headed by General Carrington. He called in the Military Police to arrest UNIT, fearing the Brigadier was in league with aliens. (TV: The Ambassadors of Death)
In 1984, an army bomb disposal squad under Colonel Archer got caught up in a Dalek plot which resulted in them being killed and replaced with duplicates. (TV: Resurrection of the Daleks)
21st century
Whilst the Battle of Canary Wharf raged in 2007, the British Army fought the invaders across London. (TV: Doomsday)
In Christmas 2007, when the Racnoss Webstar attacked London, a Challenger 2 British Army Tank acting under orders from Harold Saxon opened fire and destroyed it as its shields were down. (TV: The Runaway Bride)
In the first decade of the 21st century, the British Army were involved in a conflict in Iraq. Soldiers were killed. (TV: Warriors of Kudlak, TV: To the Last Man)
When Britain closed its borders in an alternate timeline in 2009, soldiers rounded up foreigners and took them to labour camps. (TV: Turn Left)
In September 2009, when the 456 demanded that ten percent of Earth's children be taken to them, soldiers were ordered to round up the lowest performing ten percent of the UK's children and hand them over to the 456. They stood down when the 456 were destroyed. (TV: Children of Earth: Day Five)
In 2020, Sally Morgan served as a private in the King's New Delta Squadron of the British Army. (AUDIO: Black and White)
By the 2020s, the British Army had been privatised. Certain units used performed private security work. (AUDIO: Signs and Wonders)
In 2048, after the Korven Lomax hijacked the British government and created the Department, the cyborg CCPC acted as the army of the United Kingdom, although they were referred to as a police force. (TV: K9 (TV series))
Behind the scenes
Doctor Who: Battles in Time
According to non-narrative material in DWBIT 1, in 2158, when a Dalek flying saucer attacked London as part of their invasion of Earth, the British Army sent tanks to fight off the invaders, but in a matter of days they were defeated by the Daleks.