It's a lot of money for sure. The problem seems to be that this money is so difficult and expensive to recover they don't try. Doctors have taken an oath so they will continue treating people regardless, which is fair enough.
I don't know what the solution is, I've never applied for a visa to come to Britain so I don't know how strictly they check if you have health insurance.
Anyway I agree with the previous poster in that the money we could recoup from making sure very wealthy people paid the correct amount of tax would dwarf that 2 billion per year figure.