UK, Ireland / Traveling to UK using only dowód osobisty? [7]

Question. In order to travel from Poland to England, does one need a Polish passport? Is it enough to travel on just a dowód osobisty? As far as I know, it is easy to travel within the Schengen zone on a dowód osobisty, but since England is outside of Schengen, maybe a dowod osobisty is not enough. And then would there be any problems with getting back into Poland or another EU state on just an dowód osobisty? Thanks for the help!