You do have to get an initial EASA Class 1 medical, but it does not have to be a Polish one. Do you need a Polish licence for some reason or is any EASA licence okay? Do you speak Polish?
Any EASA authority can process your training/licences conducted at EASA ATOs, with EASA examiners etc.. If you don't specifically need a Polish licence then pick an authority that is known for working efficiently, speaking good English, being practical etc. The Austrian, Maltese, Danish and Irish authorities have good reputations in this regard. I can't speak for the Polish, maybe they are good, but there will definitely be a language barrier as Poles don't have a great level of English in general.
The EASA Member State which holds your medical records will also be the state which will issue your licence.
Look for an Aero Medical Centre that has EASA approval. A quick Google search got me to this AMC in Edinburgh:
https://www.scotlandaeromedical.co.u...ass-1-medicals
Ring them and ask if they can do your EASA Class 1 and under which authority.
I believe there is another AMC in Prestwick, but I do not know whether they issue EASA medicals or only UK.