Before I get into an explanation, having gone through your source and the Strength and Casualties of the Armed Forces and Auxiliary Services of the United Kingdom 1939–1945, it seems you're confusing peak strength and total mobilised. While 8,905,000 men served in the British Army in WWI (and this figure seems to count men recruited from the Empire), its peak strength was around 3.8 million. The 3 million (~2.7 according to Strength and Casualties) for WWII is peak strength, and largely only accounts for UK troops. More would have served over the course of the war.

As for why the Army's peak strength would be lower during the second war. This is due to the RAF, which was not formed until April 1918. During the first war, the flyboys spent most of it as part of the Army. Therefore, all those men, who in the first war were counted as mobilised by the Army, in the second were mobilised by the RAF. For example, at peak mobilisation in June '44, there were 2.7 million men in the Army, and just over a million in the Air Force [1], which would put Army-RAF peak strength at about the same in WWII as WWI. It is likely more once you account for Commonwealth forces not being considered British Army in WWII.

Total mobilised by the Armed Forces however, was lower. About 5.9 million men served during the war (little under 5 million in the RAF and Army) [2]. Why could this be?

A fair answer can be found in the nature of the UK's role; in the first war, the BEF had been on the frontline in France, the main theatre of the conflict, for practically the entire duration. It had fought in some of the bloodiest battles and, even when not actively in one of those battles, had to be ready to fight one at all times.

In the second, the Army spent most of its time in Britain, or fighting on smaller fronts. With the exception of the six weeks between the German move into Belgium and the Dunkirk Evacuation, the British Army only ever had a minority of its units on the sharp end of the war until D-Day. This translates to a lesser need to keep every last soldier possible mobilised at all times as fast as possible.

More importantly, it translates to a far, far lower casualty rate. In the second war, Army casualties (dead and wounded) amounted to ~344,000 [3]. In the first, they had come to a staggering ~2,364,000 [4] (this is figures for those recruited from the British Isles, so should be roughly comparable between the two wars). This alone requires the mobilisation of many, many more men to replace the dead and the too-wounded-to-return.

[1] - Strength and Casualties

[2] - Strength and Casualties

[3] - Strength and Casualties

[4] - Statistics of the military effort of the British Empire during the Great War, 1914-1920