We seem to have drifted a wee bit from the original question which was a two parter.
First was about marksmanship standards UK versus US Army in WW2
Secondary was about speed v accuracy
Lets address the second one first.
In general any semi automatic weapon will beat a bolt action in cycle rate in identical circumstances. It's simple mechanics, physics and engineering.
Accuracy is part person, part platform and once again in general a bolt action TENDS to greater inherent mechanical accuracy than a semi-automatic.
As platforms have matured, quality control has increased etc the gap has for some narrowed now but we are still talking WW2 not 2008.
So, as a general answer, the Garand would be
capable of being faster, the Lee-Enfield
capable of being more accurate.
That's the second question mostly covered.
The first question is harder to answer due to a large number of variables.
For example, during the opening year of the war, the commonly called "Phony War" period, the BEF (British Expeditionary Force) in France were well trained, blooded, all professional soldiers, no conscripts. They were well versed in accurate long range rifle fire and had a strong NCO component with experience going back to WW1. The British Army had always focussed on and demanded all soldiers as infantrymen/riflemen first and emphasized the accurate use of the rifle.
Post Dunkirk, the army moved to a conscript force with an emphasis on getting as many warm bodies in formation as quickly as possible. Basic training was shortened and rifle training was more limited. So the new squaddie was less capable of accurate fire at the end of basic than his predecessors. However the ethos of accuracy was still embedded and they would catch up, whether they wanted to or not in a reasonably short period of time.
The earlier answer saying that Americans had a greater propensity to accuracy due to greater exposure to firearms in civilian life is somewhat disingenuous as,
The US Army at war entry was also a conscript force mostly drawn from the cities, where much of the population resided with limited previous firearms exposure
As anyone who has been in the military can attest, there's the right way, the wrong way and the military way....
.
Many recruits who would have come in with pre-existing firearms exposure would have had that beasted out of them by NCO's as they would have to unlearn old practices and habits and learn the Army way of doing it.
As a general rule the US Marines had/has the closest marksmanship ethos to the general British Army soldier ethos.
So as a general, broad brush stroke view, the UK army squaddie would have had a higher accuracy trained baseline than the equivalent US Army soldier. As time in combat increased the gap could narrow.