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In fact, Roger we don't play host to the world's asylum seekers. The US is the top destination followed by Germany, France, Sweden, Belgium then the UK. 80% of the world's asylum seekers are housed in the developing world. Research, rather than populist, anecdote, shows that the majority of those who arrive at the UK do so because they have some familial link, some language, or due to post colonial connection between their home country and the UK. The majority are not aware of the benefits system which is more generous in other mainland European countries than here. In short they are not here for benefits and, again, research has shown that immigrants are net contributors to public finances rather than a drain. There is also nothing in international law to say that asylum must be sought in the first country they reach.
I am not naive enough to believe that EVERY immigrant fits the above description but MOST do and it is important to keep a perspective. You have access to the internet - have a quick search and get a broader view.