The UK driving test is significantly more rigorous than the US, and it shows: UK drivers are amongst the safest in the world (2nd lowest road fatalities per 100k people; top five per 100k vehicles). The US isn't even in the top fifty (and for calibration to the American reader: Canada is in the top 30, but hey, at least the US beats out Mexico). At the end of the UK practical examination process I would expect all new drivers to be "competent" by this standard.
As a Brit, though it would be nice to think we drive better, I think most of the effect is down to road engineering. Roundabouts have lower fatalities than traffic lights for example.