Full-scale integration will NEVER happen
The UK's immigrant population is growing like crazy. One in five residents of England are born abroad. The ethnic English are shrinking and being told they don't have a right to their homeland, by people who protest all day about Gaza. Even moderates are indoctrinated into not recognising their right to their homeland, where their ancestors have lived for thousands of years.
With the immigrant population rising and the native population shrinking, there is no incentive to integrate. The less immigrants there are, the easier it is for the host country to integrate them. However, do you seriously expect someone from Pakistan to be suddenly enamoured with UK culture? Even their kids want to marry into the English population, yet their families will handpick people from Pakistan for them to marry and bring over (as well as their partner's entire family, probably). This is clearly an issue.
If I were a Serbian moving to Norway, people would expect me to learn Norwegian, adapt to their behaviour, embrace the Norwegian culture, and to leave incompatibilities at home. I wouldn't be loudly Serbian, only make friends with Serbians, and complain Norway should be more Serbian. However, the suicidally tolerant Brits feel no problem letting people arrive and actively seek to change our way of life. Surprise, surprise, this is only a problem among immigrants when you go further and further from Britain. The French don't have an issue here.
With how things are going, it will soon be of no interest to politicians to advocate for English concerns. By that, I mean putting foreign interests above English ones, e.g. allowing more mosques to be built, more community leaders of foreign communities, defining Islamophobia in parliament, basing votes off a foreign war that doesn't remotely concern us etc.