The Allies were in no position to send any amount of ground forces to assist the Soviets on the Eastern Front. Not only was the British Army preoccupied with operations in North Africa and the Mediterranean at large (and later the Pacific theatre), but the American military had not sufficiently "geared up" to provide actual boots on the ground in a way that would benefit the war effort in the East. To put it bluntly, "in 1941, there was no chance of a Second Front [...] Britain and the United States could only hope for Russia's survival while they calculated how best they could together distract Hitler from his campaign of conquest in the east and weaken the Wehrmacht at the periphery of the German empire". Thus, the British intervention in Greece, Norway, the North African campaigns, the need to protect Egypt and the Suez, and eventually the (contentious) decision to strike into the "soft underbelly" of occupied Europe via the Italian peninsula is what resulted. By the time major ground forces were available to the Western Allies, there was no strategic need, ability, nor desire to deploy them to the Eastern Front.

There are more factors at play here, including the tension between Anglo-Soviet relations in 1941-42, the questionable benefit (if there is any) of sending a handful of Anglo-American divisions to the Eastern Front, the difficulty in supplying those home divisions in the context of a foreign war in a foreign nation, and the likelihood that Stalin, while "desperate for the sort of supplies only Western industry could supply", almost certainly did not want American or British ground troops on Soviet soil.

It's safe to say that whatever ground forces could have been mustered and somehow transported to the Soviets would have been relatively pointless in the context of the Eastern Front; Stalin didn't need a handful of British blokes from Liverpool or ten divisions of eager American boys, he needed British and American trucks, aluminum, foodstuffs, and dozens of other industrial resources that the Soviets could not produce due to the loss of the western parts of Russia and Ukraine, some of the most productive land in the entire USSR, or simply lacked the advanced industry to do so in the context of a war where the Soviets had quite literally dismantled hundreds of factories and shipped them east.

In July of 1942, the Allies agreed that the "opening of the 'Second Front' had been definitively postponed from 1942 to 1943". North Africa and Italy were useful battlegrounds in chipping away at the edges of Germany's empire, but the true Second Front wouldn't come till later. While the invasion of France would eventually be postponed until 1944, it is important to note here that Stalin desperately wanted the opening of a Second Front because, strategically, he needed to pull at least some German divisions, men, and resources away from the Eastern Front. While its possible that, if the United States had been able to focus solely on Germany, there may "have been less delay in opening a Second Front directly against the Atlantic Wall", it's hard to imagine the Anglo-American forces launching any major land offensives in continental Europe until 1943 at the earliest. At this time, of course, the tide in the East had turned against the Germans (you can pick your specific turning point, be it Moscow in '41 and Jan. of '42, Stalingrad, the failure of Case Blue, Kursk, god knows how many books have been written on it) and any "need", if there ever was one, for western ground troops to assist the Soviets on their home turf ceased to exist.

All that said, the Soviets did make use of Polish soldiers in the form of communist puppet organizations and I do believe a fair number (not sure how many) Poles fought for the Soviets, but I don't have numbers on hand and it's debatable if you want to count them as "Allied ground forces" in the context of the question you're asking.

Sources: Keegan, The Second World War

700 million tons of fuel were pumped across 20 130 km long pipelines that were laid under the Channel in order to support the European invasion. Mulberry harbours were created to enable the British and American forces to disembark in sufficient quantity. Imagine laying this pipeline to Murmansk and then having these harbours towed there. The pipeline alone would be a decade-long task in peacetime, and completely impossible if every U-Boat in the Atlantic was headed for such a huge and juicy prize.