Young people in the UK seem less bothered about passing their driving test at 17 - university is ahead of them, so there is no point putting money into a car - I went down this route, and am now 27 and still don't drive, and cannot see this changing unless it becomes essential to work or family. The roads are so congested where I live that the car is no longer a symbol of freedom like it had been for my parents.
The UK has a much more effective public transit system than most of the US. Also, the distance scale there lower than it is in the US. These factors together mean that changing driving patterns in the UK may not be matched in the US (personally, I know of anecdotal evidence in both directions, so I expect the difference in the US to be very regional).
By area, most of the US is hard to serve with mass transit. But by population it's tractable -- you don't have to lay bus/rail mesh everywhere, only where it's already dense. The 10 largest metro areas in the US are about 75% the area of the UK with a population 5% larger.