The thing is pretty much no one pays the full price at Harvard.
Most UK universities also charge around 15-25K GBP a year for foreign students so if you want to compare apples to apples there really isn't a big difference. UK Tax payers pay heavily to subsidize cheap university education, with mixed results. I believe that every one should have a right to university education and not be excluded on the basis of cost (only ability). But people shouldn't go to university for the sake of going to university as Labour tried to sell. People should go to university because they have an ability and a university education would benefit them and the country, not burden the tax payers.
The US has a student loans system that runs very similar to the UK- low interest rates and payments taken form a salary (it is also tax deductible). Thus what really happens is students rake up some debt which they pay off once graduated. The student must decide whether the degree costs are going to be rewarded by increased salary. For a graduate of Harvard in something like Computer science they can walk into a job at over 100K a year in the Bay area and have their loan paid back in a few years. Other degrees may not be that financially dependable.