Your last paragraph is a Godwin point. The first thing that would avoid a war between EU and UK would be tolerance for their point of view with a discussion about immigration without everyone throwing arms in the air and saying "they're all fascists" (which I have heard this week with a lot of anti-british hate).
Yes, immigrants who have been accepted are all UK nationals and they belong there now. Now have we asked the country side UK people whether they want to distribute more visas in 2017 to non-EU, highly skilled, foreign workers, followed by a passport in 10 years? I'm being specific here because liberals tend to conflate xenomurderers with people who want a honest discussion about visa quantities.
Same thing in France. We are still allocating tens of thousands of visas to non-skilled non-refugee immigrants: "Family" visas - aka get your brother in, and all your family can immigrate. We also have the free hospital policy and we've made mistakes with massively accepting people for medical tourism. I have nothing against existing French nationals and I have been the first one to protest aside them against police/administration racism. But we haven't succeeded the battle of the ideas and, as you mention, we have created terrorists out of native French citizen who were exposed to racism. Whether it's the school which isn't free enough, or there university which isn't free enough, or the taxes for the poor which aren't low enough, or specific language/culture classes which don't transmit or values, there is a failure in our integration process. And until we guarantee that we integrate newcomers with our values, I want to postpone non-mandatory immigration as long as there's not enough budget for their teachers.
One of our values is that you, as a French person of 2nd generation, teach your kids to not burn the flag of the country you're in. Another is that we've fought for a century so our women are free, so there will be no sign of submission in women (and the church needs to align too). Another one is, if you're in, don't swap your PhD for smuggling 10k€ of illegal goods after 3 years (which I've seen). Another one is that school is free, so your son better work hard before you complain about racism.
Oh and before you complain more about racism, if I invite you home for programming lessons, don't touch my 8-year old niece (which I've seen). The guy didn't even go to jail, he was merely told off in a police interview with his parents (he's 16). I didn't want to say there's an anti-white movement, but when that happened, in 2015 and together with the two Paris attacks, I started wondering. And it's time we reset equal rules for everyone.
So there is a political question to answer, in every country, about how many visas we issue in each category, how we proceed to integrate everyone, and still make it fair for countryside people. And as long as the liberal answer is "Welcome everyone, all criticizers are racists!", then the answer will be... racism.