This was a long time ago, but a relative of mine was hiking in Wales, and got injured. She made it to the next town and found a clinic, where she was treated. Then she asked how she should pay. They were like, pay? You don't pay for medical care.
She told them that she wasn't from the UK and therefore wasn't covered by their system. But they said that they had no way of figuring out a price or generating a bill for her. So she went on her merry way.
The short version is that primary care services like consulting with a GP, visiting a walk-in centre, or emergency treatment in a hospital accident and emergency department are generally free to all, as are various other specific types of care.
Most secondary care services such as other hospital treatment are only free to people ordinarily resident in the UK, which roughly means anyone who is an EEA citizen or who has the immigration status of indefinite leave to remain, again with lots of other special cases.
Some services, such as dental work and buying prescribed medication, are generally chargeable by default for everyone, though even then the NHS may set standard prices and there are various provisions to help those of limited means or in certain vulnerable groups.
But yes, if you have a nasty accident and need to go to hospital as a result, no-one is going to be asking for your credit card number here before sending the ambulance, and if you only need treatment in A&E and don't need to be admitted as an in-patient, you probably would get most or all of your treatment for free even though the equivalent in certain other places would cost a fortune if you didn't have insurance to cover it. There are a lot of reasons we are proud of our NHS here, and this is one of them.
Just in case anyone reads this later, let me add a final note that if you're coming here, please check the details for exactly where you're planning to visit. A lot of health policy is devolved, meaning policies can be different in England from in Wales, for example.
She told them that she wasn't from the UK and therefore wasn't covered by their system. But they said that they had no way of figuring out a price or generating a bill for her. So she went on her merry way.