British Expeditionary Force
The name given to the part of the British Army of old used for fighting war rather than colonial policing, recruiting and training or garrison duty, in both World Wars.
The BEF of the First World War was small and professional at the start. It paid an extremely heavy price in 1914 holding back the numerically (by a huge factor) German advance while the Army was desperately expanded and Territorial units mobilised. Along with French forces, it fought successful actions at Mons and the Marne, halting the German forces long enough for the Territorials to arrive and take over the line -- and recieve a hammering instead. 1915 saw German offensives at (Second) Ypres repulsed and failed offensives at Neuve Chapelle and Loos -- one due to lack of shells and the home front failing to supply the Army well enough, t'other due to reserves being held too far in the rear and failing to exploit initial successes.
By 1915, the new battalions of 'Kitchener's Army' were arriving in France and being deployed into quiter sectors. In 1916, they were put to their first full test -- The Battle of the Somme. A horrendous, bloody slog, lessons were learnt and the BEF bloodily relearnt its trade.
1917, saw the BEF more or less fighting alone, as Russia suffered catastrophic defeats and then revolution, forcing her out of the war The French, fed up with awful conditions and repeated defeats, mutinied. While the mutinies and their fallout were dealt with, the BEF remained the only active army. It carried out several large offensives , all of which had promise but ultimately failed; the most iconic of these was the Third Battle of Ypres / Passchendaele. In fact, the offensive progressed well at Ypres, and things looked a but iffy for Fritz, but, as one German Officer later wrote with considerable relief, 'Then the Rain fell.' The offensive stalled in liquid mud and another bloody battle of attrition took place. Some of the most iconic photographs of the war, of troops struggling through waist-high mud and for which generally seem to represent the war to most people in a nutshell, come from Passchendaele.
1918, thanks to an influx of victorious troops from the Eastern Front, saw the Germans launch a devastingly effective assault known as Operation Michael, or the March offsensive. Using Stormtrooper tactics and heavy artillery, they blasted a hole on allied lines and caused the Entente forces to retreat - mobile warfare resumed for the first time since 1914, with British and French troops in retreat. This was finally halted at the Marne -- rather like in 1914 -- and the British and French prepared to go back on the offensive.
Under the leadership of Field Marshal Douglas Haig, C-in-C since December 1915, and his subordinates, Generals Rawlinson and Plumer, the British army went back onto the offensive and smashed the Germans at Amiens and began to advance continuously in the 'Hundred Days' campaign, which broke the German Army and forced them to seek an armistice.
The BEF ended the war as the most advanced fighting force in the world at the time. They had - at a bloody cost - explored and developed the principles of effective modern combined-arms warfare, with the RFC (and then RAF) working in close cooperation with ground forces, with infantry seamlessly cooperating with armour, and artillery being able to be used with great effectiveness due to better communications. This was an army that even had self-propelled howitzers and armoured supply vehicles and APCs (converted mainly from Mk IV tanks), which was extremely forward-thinking for the time. The Germans had to station around half of all their divisions against the 120-mile (or so) front of British lines, compared to 300+ miles of French lines.
It is a terrible shame that a lot of the lessons learnt and forward-thinking ideas that were developed here were forgotten by the British in the inter-war period. Unfortunately, those who were on the recieving end of them took note...
The BEF of the Second World War had been once again reduced in size considerably to a small, professional force. Although it was the only fully mechanized force at the beginning of the war, it had forgotten many of the principles learnt the first time around. It was sent across the Channel at the outbreak of the Second World War to help the French stop the German Blitzkrieg.
Although well trained, they were not equipped or ready for the modern combined arms tactics of the Germans, and with only the support of the French, they found themselves fighting a series of delaying actions and being evacuated from Dunkirk.