It appears to me that Britain's real contribution in WWII was the quality of troops, rather than the quantity

I don't think I would say this; there were serious morale problems in the British and Commonwealth forces in WWII, the Desertion Crisis in in Italy in autumn-winter 1944 being a striking example. In Normandy, morale plummeted in the weeks following the invasion, especially in between Villers-Bocage and the conclusion of Operation Goodwood. Although it greatly improved afterwards, and remained classified as 'good' or 'very good' by mail censors until the war's end, Monty's operational method ('Colossal Cracks') was designed to maximized firepower and assign limited, achievable objectives, so as not to greatly tax the morale of the Infantry. This ties in neatly with the rest of your question actually:

why wasn't the UK/Britain able to mobilize more substantial a fighting force in WWII, especially considering American support?

As John Peatty demonstrates in his [thesis] (https://kclpure.kcl.ac.uk/portal/files/2931337/313385.pdf), by 1944 the British Army was facing a looming manpower crisis. The overall quality of the Army's available manpower was not as high across the board as it had been in WWI, when the Army (specifically the BEF) had had priority for manpower, and had been the primary armed force in need of it aside from the Navy. In WWII it was different, with the RAF and the Royal Navy taking priority due to the U-Boat menace and the lack of a major land campaign, while the increased demands of industry to supply shells, tanks and transport for the ground forces, aircraft for the air force, and ships for the Navy and Merchant Marine meant that there was a third major competitor to the Army. There was also competition within the army, between regular infantry and the artillery, tanks, and elite units like commandoes, chindits, and paratroopers. Combine this with the geographic separation of the various fronts that occupied significant British forces, from 1944 onwards Northwestern Europe, Italy, the Middle East and Burma, meant that the British could not maintain a significant concentration of forces in one theatre as they did in WWI, where 60 British and Commonwealth divisions were in France and Flanders, with Mesopotamia and Palestine the only significant diversions.

Nor did they need to; American divisions far outnumbered British divisions, and with the growing supremacy of the United States in the Anglo-American alliance by 1944 it made sense that American forces would contribute the bulk of Western Allied divisions in Europe. This still does not belittle what British 2nd and 8th Armies, and 1st Canadian Army achieved in Northwestern Europe and Italy, or 14th Army in Burma.

I'm not entirely sure what makes you think they didn't, as a portion of the population. Troops from the home country were fighting the Germans in France, the Italians in Africa, and the Japanese in the Pacific. To add to those, you saw divisions from Canada, South Africa, Australia, New Zealand and India in Europe and Africa. By the end of WW2, the Indian army was over 2.5 million strong.

Other dominions threw in as well, combined. West African colonies sent two divisions, The East Africans sent one. The Carribean threw in what they could, but given the population, it was more local support. Population about drives the lot of it. Remember that the entire population of the continent of Australia was only 7 million, of all ages and skills. Canada's population was about 11 million, of which 1.6 were in uniform.

You may not hear much about them, because the Burma theatre doesn't get much press in the US, neither do you mean much about the Australian struggles against the Japanese before the US showed up, but the Commonwealth was definitely pulling its weight.

To add to DuxBelisarius...

One reason was World War One. Britain was most reluctant to go to war and was strongly anti-war in the 1930s, and this affected her policies on a number of levels.

Many jobs were 'protected' and efforts to recruit everybody possible were more limited, both officially and in terms of social pressures. Britain put a massive effort into the Bomber Offensive which it was hoped could win the war without a land campaign. This effort was industrial and in technology and investment, and took many men (though fewer than an equivalent land army).

The (white) Commonwealth nations followed the British with enthusiasm into the Great War, but the massive losses produced a similar reluctance on their part 25 years later. Australian troops had to volunteer for overseas service, and the Australian government was reluctant to use militia (reserve) troops except in the direct defence of Australia: MacArthur was later happy to sideline Australians into bloody mopping-up operations.