I don't think it's a battle.
I've seen first hand that as the generations progress, each iteration begins to act more and more like the host nation.
Young Muslim women going off to University to study Law and enter Beauty Pageants are things their mothers and grandmothers would've never dreamt of. This is the result of growing up in Britain.
My great grandparents on my Fathers side were Polish immigrants who fled the Nazis. I have almost no ideological connection to them, despite them being blood relatives. The same goes for Indians who migrated in the 60s and the Afro Carribean communities who migrated in the 60s and 70s. Whatever the modern, prevailing culture is at the time engulfs all into an amalgamated culture. We have problems with Muslim integration, signs that Muslim women are going off to the highest sections of education and entering beauty pageants is a massive sign of progress for that community integrating into modern British society.