Despite what it may seem, most countries do not have infinite debt. In fact, the number of countries in the world that have a fiat currency in their control is very limited.

Greece is a good example of this. No country in the EU has direct control over the Euro. So no country is permitted to just print their way out of debt unaccounted for. So when the Greek economy was crashing and the rest of the EU was strong their currency didn't devalue with their economy causing a crisis where they could not pay bills.

The US tends to be a bit of an outlier in the world in terms of currency. Since US currency is traded all over the world it's not entirely dependent on the US economy to maintain its value. This allows Congress to authorize printing a lot more currency than they might be able to because a very high amount of US currency is being traded between other countries. That doesn't mean the US has no upward limit (a debt ceiling) for how much they can spend. But it does mean that ceiling is a lot higher than most countries.

But for most countries in the world the more debt that you have, the more devalued your currency is, and the less debt you have the more value it will have (assuming all things stay the same). When a country like Britain is weighing spending their primary concern is devaluing their currency too much and making the costs of importing goods too expensive for its residents.

Sometimes this is known as the Devaluation Spiral. You print more money to pay for more things and the value of your currency goes down. So the next year in order to maintain spending you have to print even more money to pay for more things... and the value of your currency goes down. And the next year in order to maintain current spending you have to print even more money to pay for things.

And you don't want that.

As for why the UK doesn't spend more money on healthcare, it's because the people in power prioritize other spending.