It is worth noting for clarity that there is no "British health system" – the constituent nations of the UK have separate and distinct healthcare systems.

In reality, "negative stories" aren't much of a strong signal. There are likely as many "positive stories" that don't get as much traction, particularly because there is quite a lot of effort invested in the US into spreading FUD about single-payer healthcare systems. Though I do agree that this effort is effective on many people.