This is such a complex process. I've been studying migration over the past 5 years and being an immigrant myself my views can be a bit bias.
Generally, immigrants have a negative connection on how they put pressure on the hosting society. In fact these pressures are real, but on the other hand immigrants contribute a lot to the society. Most immigrant fill the gap in the labour market of the so called 3D Jobs "dirty, dangerous, and difficult", have low waves, work long hours and are more exposed to a fragile working market, being many times explored. However, there is also a small percentage of high educated immigrants, which do not have good working condition in their home countries and are forced to migrate to use their skills. In a sense, the country of origin suffers a "brain drainage" and the host society received people with high skills and, and did not spend any money in their education. Also, as mentioned by some in this thread, British citizens are also migrating to other countries, being, part of a phenomenon called International Retired migration, where older people by housed in sunny places and live there most of the year
The pressures in the population.... well... population all over Europe is getting older, therefore migration is welcomed. In Scotland, for instance, population grew due to migration and the new births, otherwise the balance would have been negative.
Different countries have different ways to deal with the arrival of immigrants, and to be honest I think the UK has done a very good job, in comparison, for instance with Germany and France. Very broadly and superficially, In France if you are in immigrant you are expected be behave like a French, embrace their culture and values and live your own cultural identity aside (see the example of the veil). On the contrary, in Germany immigrants are seen as immigrants and therefore live aside of the German culture. These two different position have lead to the same: exclusion! it is true that multiculturalism has it problems, but at least it recognises individuality and tries to incorporate immigrant in the host society.
As an immigrant in the UK, I must say I've been having a very good experience. I also make an effort to live outside my "cultural bubble" and try to be part of the community and contribute to the best of my abilities. I've learned so many good things in this country, and I'm grateful for that.
In my opinion it takes time for the immigrants communities to blend in the host country. Many may want to keep their individual culture, but what is essential to assure is that these communities are not marginalised and have the opportunity to be included. I would add that special attention should be focused on the children that are born in these country, because they will be the future generation and they should not feel segregated as previous generations.
Sorry for the long post