See, here's the issue.
NHS and other non-US markets negotiate prices with drug companies, often forcing them to sell those medications at a loss or lose access entirely to that market. In order to make that loss back, they have to shift the cost of the drug to markets who do not force pricing - especially the USA. That's one big reason why the US has jacked up prices - we are effectively subsidizing medical treatments for the rest of the world.
When you implement price controls and force a producer to sell something at a loss, they have to jack up the price elsewhere, or else go out of business. TANSTAAFL.