Yes indeed, the Polish really helped a lot. But obviously they could not continue their efforts after Poland fell -- not in Poland anyways. And everything else you say is also true. The last thing you say is particularly insightful: that the U.S., by using commercial contractors, was essentially committing to letting them commercialize some of the technology, while the UK by not using commercial contractors, was not and then did not. It's especially sad that homophobia led to the early end of Turing's life -- imagine what he could have done had he lived longer!