The first thing is that the economic success that Britain has enjoyed has been helped immensely by immigration. How else do you cope with demand? In theory the immigrants are quite happy doing the low paid jobs that others don't want to do. Whether that keeps wages artificially low is a moot point. Merkel is currently doing the same in Germany to fuel their worker shortfall. History will show that her universal welcome was a bad milestone in Europe.
Where it falls down is in two areas.
1. Documenting who is actually arriving. I am afraid it is high time everyone has an ID card linked to their healthcare status and employment status and bank accounts. Law abiding folk would have nothing to fear. Britain steadfastedly avoids this from some trivial concern over "rights".
2. Trying to integrate newcomers rather than allowing them to impose their beliefs on the indigenous people. Hajibs, Mosques, minarets and so on. Ask yourself would Brits be able to wear short skirts, sun bathe topless, build Protestant churches if they went to live in a Muslim country.? I don't know how you stop like minded nationalities congregating in certain areas and making them no go for other nationalities. It is human nature. We Brits do the same thing in Spain. Don't learn the language, set up British goods shops and all day English breakfasts, complain that the shops shut for siesta and so on. Our vet hates the Brits that greet her with Hiyahh. She says why can't they use a Spanish greeting.
It is a funny thing but we use a lot of black pepper and buy it in 500gram bags from the Indian shops on Evington Road in Leicester when we were back in the UK. Well we don't now as the last time a bunch of West Indian women in the shop made Mrs V very uncomfortable. Did the stop talking in a foreign tongue thing and actually questioned her on what you want in here honey.
Think of it as like the fall of the Roman empire. They (we) got too well fed , lazy and complacent and lost it.