No, Poland is not part of the United Kingdom. They are separate sovereign states with distinct histories, governments, and geographies.
Poland and the UK were WWII allies (Polish forces fought under British command). Post-war, Poland fell under Soviet influence; the UK helped establish NATO. Since 1989, both are democratic allies in NATO and (until Brexit) the EU. Large Polish diaspora in the UK (~700,000).
Confusion sometimes arises from migration ties or WWII history, but politically and legally, they are entirely independent.