You asked for reasons, I'm giving them to ya, Its the equivalen of an already sinking lifeboat taking on a cruiseliners passenger compliment and expecting to stay afloat.......
Give me a good enough reason not to include em and i'll happily withdraw them 
I'll give you more than one...
1/ the UK takes in 1 refugee to every 317 people; less than the european average. The asylum application rate is also less; we have 1 in a 1000, the likes of Denmark and Norway have 3-4 per 1000. These particular Scandinavian countries boast some of the strongest economies in europe, and also have some of the highest asylum acceptance rates.
2/ We're also well down the table of countries accepting refugees, too; Iran is actually 1st (!), with the USA and Germany in particular ahead of the UK (which ranks about 32nd). Our (averaged) acceptance rate is 34%, less than the likes of Canada or Denmark.
3/ As of April 2003, there were 1,396,000 overseas
workers in the UK, and less than 50,000 asylum applications (only 23% of whom were give permission to stay). Neither represents a significant enough number to be made scapegoats for social changes. 10% of British GDP - more than North Sea Oil - is attributable to migrant workers (income tax from said workers also is £2.5bn more than is spent on immigration; FYI more than twice more is spent on arms subsidies - £900m - than on asylum seekers - ~£440)
4/Asylum applications across europe fell 40% last year. Despite the Sudan conflict (for example) displacing over 4m people, the number applying to the UK was....930.
5/ Asylum seekers are also more likely to be qualified for work than the general population; i.e. 53% have academic qualifications)
6/ 80,000 asylum seekers are on the NASS benefits (which is less than both the dole and below the poverty line); 15.5m are on benefits. That is, a whopping 0.5% of those on government support are asylum seekers. I'll note that asylum seekers are not allowed to work.
In other words, this suggestion of being swamped by immigration is complete and utter bollocks, which is disproven by any number of statistics. We treat asylum seekers like ****, and then blame them for society. The net population rise to immigration since 1997 has been a million; that's less than 2% by my hand-wavy calculations, and we
need relatively young foreign workers who'll come in, give income tax to prop up the likes of pensions, and then go back home after 10 or so years (as most of the eastern european immigrants do).