I think most ethnic minorities I know don't really intergrate with British people as much. It's mainly work and school. But when it comes with building communities it's building community centres, mosques, temples and etc. In Birmingham for example there are loads of asain people in picket areas and not really spread out. It's just the way if is. They don't hate England they actually prefer it to their ansestors country due to opputurnities. But just can't intergrate enough for example lots of etchincs don't have a drinking culture and never would see them in a pub.
I think when it comes to sports, it depends if there is a viable option for minorities or immigrants to root for instead of the home team.
In Canada, most people root for the home team for hockey, second option is any Canadian team, third option is a US team. That doesn't mean Leaf fans cant hate Habs or someone wants to cheer for Boston (Boston is probably the most liked US team) . But that's a typical pecking order. Nobody roots for some no-name league in another country because Canada wins or makes the finals in most tournaments and most countries dont even play ice hockey anyway even if they scrape up a team for a tournament as the 16th best team.
For basketball, everyone roots for an NBA team. Mostly Toronto Raptors, second is probably Lakers, Celtics third. There's good European and South American leagues, but I have never heard anyone bring up those leagues ever.
For soccer, even though EPL, and whatever Italian and Spanish leagues have the best teams, people probably cheer for weak country teams because the sport has enough decent teams and leagues around the world and teams probably have enough semi star power because some of the players play in well known leagues, so there's something to root for.
The sport is low scoring as a whole, so even a team getting dominated may only lose 2-0. So on the score sheet it still looks close, so cheering for a country team that wont go anywhere is still a close game.
In basketball, the US team wins almost every match by 30 pts and weak teams in hockey lose 9-0. Hard to cheer for the weaker country team when it's a disaster after the first half an hour.