THE UK card is not for 'normal health care' in another country. It is for 'emergencies only' in another country.
It's not really for emergencies only. It's for any treatment you may need from the medical point of view - but not planned treatment. If you, for example, need some kind of an operation, but it's nothing urgent and you can wait with that, you should return to your home country to have it.
The limitation is that this card (EHIC in English, EKUZ in Polish) works only if you are abroad for touristic purposes (and then it's validity is limited to a few months), or you are on an exchange as a student. Probably also if you are employed in your home country and going abroad is a part of your job - I am not sure about that, but it seems logic. It does not work, however, if you are employed in a different country. Then you are subject to the healthcare system of this country and you cannot use EHIC. Or, at least, you shouldn't and it's illegal to do it - in reality it might be possible.
If you are in Poland, you don't have any job (or you work on basis of some types of civil law contracts instead of a normal job contract), you are not a child, not a student, not retired and you are not registered as an unemployed person, then you are right, you don't have any insurance, unless you pay for it voluntarily. If you go to any doctor - you have to pay, and in case of an accident, the emergency and the hospital will issue you a bill.
It applies to the Polish nationals as well, not only to the foreigners.
But in such a situation - from the moment when you become not employed any more - you may be able to get EHIC from the UK, as a tourist. I am not sure about that, though. Maybe there are some restrictions on that and after beying employed in a foreign country, you cannot be treated as travelling touristically to this country in the UK.
BTW car accident is a special case, because then if you have to pay for all the medical treatment, the payment will be anyway covered from the civil liability insurance of the car with which the accident was caused. Unless no such person was determined - then you have a problem.
But in such a situation - from the moment when you become not employed any more - you may be able to get EHIC from the UK, as a tourist.
Maybe there are some restrictions on that and after beying employed in a foreign country, you cannot be treated as travelling touristically to this country in the UK.
After a while of rethinking - no, you cannot since you are not insured in the UK. Unless the British regulations give each citizen right to free medical treatment regardless of whether they work or not. Theoretically it might be so, and I have no idea how it is in the UK.