integrate more strongly with Britain and weaken your links with Poland
You can integrate with one country without weakening links with another.
It's isn't 1930 when contact with home involved a short wave radio and a three week wait for letters to arrive.
London and Warsaw are closer than London and Inverness or Warsaw and Szczecin, and there's no pressure to assimilate or reason to do so.
In my city in the U.K. there are thousands of people who came from a Poland post-2004. Some choose to integrate, most don't and don't need to. Those who integrate either have a hobby which brings them 8th contact with people, a partner they met in the U.K. or they were still school age when they came. The younger ones are sometimes more British than Polish however there is no pressure on them from society.
Water finds its own level and all,of us migrants find our niche. Either assimilating, living in an expat bubble or most often on a continuum between.