The postgrad v. undergrad comments are true (a lot of people take top JDs once they are already earning or have been sponsored to do so), but there are still massive differences at undergrad level.
Its really down to the influence of government. The US government doesn't limit the prices of US universities. Tuition fees are capped at 3k p.a. for EU students, with the government adding a hefty subsidy.
There's also a culture difference. In the US, parents typically save for their child's college education from day one. In this country, you get people whining about how its unfair that they don't get EMA because they think their parents won't pay anything to them - middle-class parents take a lot more financial responsibility in the US, whether it be saving for college or choosing to live in areas with high property taxes so that the schools are better (in the US, state schools have different levels of funding based on how local property taxes are set). Its accepted in the US that if you don't have parents able to save enormous amounts of dosh for you, then you will only be able to go to a local community college subsidised by your state. In the UK there is a lot more emphasis on individual opportunity: it wouldn't be politically acceptable for universities like Oxbridge to set prices such that the poor were denied the opportunity to go there - the government have made truly enormous moves to widen access over the last 12 years; it now wouldn't be politically acceptable for the Conservatives to oppose it in the same way that they did during the 90s.