I’m not at all sure what it means, though.
If you asked some very devout and devoted Christians if they think of htemselves first as Christians or as Americans, what would they answer?

Terrorism has also served to separate Muslims into their own psychological and social enclave, as I suspect,and many have expressed., Being aware that they’re looked at with fear and suspiciton, there would be a natural tendency to circle the wagons and to stick with the safety and acceptance of their own kind. There might well be a push and pull aspect to all this.

But beyond all that, I’m not sure how being inegrated is defined. In the US, for example, there are segregated neighborhoods, schools and social groupings. Actively seeking integration and diversity is increasingly met with strident resistance.
Are there parallels between race relations and the situation with Muslims?

The bottom line question is about loyalty, I presume.
To get to hat issue through the prism of integration requires more in-depth study, the kind summay overviews can;t provide.
This would seem to be fertile ground for budding as well as established sociologists. I thope many of them turn to it for much needed study. We all talk about it, wax eloquesnt about it and form definitive opinions about it, but no one really understands it, IMO. .

Still, I think that in order to make the results really significant, they would have to be done for “British identity” and not so much for “Muslim identity”. I’m fairly willing to believe that the stronger the Muslim identity the weaker the national identity, but it strikes me that this correlation probably has a lot of exceptions. As far as how potentially dangerous non-integration of Muslims is, I think it’s so for those who don’t really feel connected to the country they live in. I wouldn’t be surprised that if you felt “very British” you’d be no danger to anyone, no matter how Muslim you felt.