This is a nice question. I can only answer theoretically. Yes! Since Poland is a EU member state, then you should be able to, as long as you are certified to practice in Poland.
This means that you should graduate from a program in Polish, or at least pass the Polish state exams. Then it is a question of whether you will be able to secure a residency position in the UK or Ireland, and then if a hospital will be willing to hire you. In a certain sense, this is similar to the situation in the US. Graduating from a medical school does not meant that you will get a residency, and that you will get hired later. I hope that someone will be able to provide a better response than mine.
I think though, that simply because of sheer size, you will have a bigger chance of getting a residency in the US, provided you have good board scores.