It absolutely has to do with the kinds of warfare that was experienced during each conflict.

As you probably know, the First World War was characterised by the predominance of trench warfare, continuous lines of excavations and earthworks from the Swiss border to the English Channel. For four years, the British (and commonwealth) held a significant portion of that line, almost everything to the north of the River Somme. This exposed the British troops occupying the line to shell fire which while not always heavy, still inflicted casualties. Additionally, the British not only participated in very large offensives, they very often spearheaded them or launched them by themselves as with the Third Ypres Campaign. Due to the inherit nature of trench warfare, offensive operations almost always incurred heavier casualties for the attacker and the British suffered heavily during all of their major offensive operations. Again, the nature of trench warfare left very little opportunity to mitigate casualties due to the inability to manoeuvre. This left large concentrations of men susceptible to the destruction wrought by modern weaponry, particularly artillery which inflicted the majority of casualties during the war.

Compare this the the Second World War where the British largely (but not always) fought wars and campaigns of manoeuvre. North Africa in particular allowed for large tactical manoeuvres which prevented large concentrations of men coming uber enemy fire for sustained periods (for the lost part). After the entry of the United States, the British Army began taking on a more subsidiary role due to manpower restrictions and its need to provide forces to its multiple theatres such as India, Burma, Malaya etc. this is not to say that the British Army didn’t play a significant role in defeating Germany, they bore the brunt of the fighting in North Africa and played not insignificant roles in both the Sicily and Italian campaigns but unlike in World War One, they never faced the bulk of main German army, that tragic distinction goes to the Russians. Even after D-Day in which the British played an equally significant role as the US, the British took on a subsidiary role to the main US thrust, restricted to advancing along the coastline and into Belgium. Again, Market Garden would see a surge in British contribution but after the failure of that operation, the US pretty much took over the advance towards Germany and bore the brunt of the casualties.

I want to make it clear that my post is not intended to disparage the contribution made by the British Army during the Second World War but to point out that unlike in the First World War, the British didn’t bear the brunt of fighting the main body of the enemy during the Second and by the time that significant operations could be conducted on the continent, the British contribution had been overtaken by the United States.