Arguments both for and against open immigration often take place in ignorance of the economics of immigration. It's important to recognise that immigration has enormous benefits to indigenous populations as well as immigrants. (Full disclosure: I am an immigrant from the Republic of Ireland, but I've contributed a lot more in taxes than I've used in services.) As Bryan Caplan has argued , immigrants allow a greater division of labour in a country, effectively bypassing trade barriers, and drive per capita production upwards. Technological advancement and the entry of women into the labour force have displaced workers and created frictional unemployment, but created large long-term increases to per capita income. The same is true of immigrants. Any argument that immigrants create unemployment uses the same fallacious logic that open trade makes us poorer.
This argument is sometimes countered by the claim that immigrants will simply become net drains on the welfare state. Even if this evidence pointed in the other direction, it would be an argument against the perverse consequences of the welfare state rather than against immigration. But it is simply not borne out by empirical evidence, which (in the UK) suggests that immigrants have a higher labour force participation rate than the indigenous population and a lower per capita utilization of public services. A 2007 Home Office report (PDF)  found that immigrants’ net contribution – that is, taxes paid minus the cost of services used – is equivalent to one percent off the basic tax rate. Immigrants are subsidizing indigenous welfare users. (See also this 2002 study  with similar conclusions.)
To those concerned about "brain drain", immigrants send huge amounts of money home in the form of remittances. The development economist William Easterly says that remittances are a great way of relieving poverty in poor countries, because they pervert incentives less than NGO aid and don’t carry the same risks of corruption that bilateral aid does. The only long-term solution to developing world poverty is free trade and good governance in those countries, but open borders are a good step too. Does, say, Vietnam really benefit from its most talented people being wasted in rice fields? I would say no – better to unlock those talents in Western economies and let some of the benefits flow to that person's family back home.
Yes, there are other issues associated with immigration, like the preservation of indigenous culture. As a libertarian, I don't believe that it's the state's role to try to influence or protect culture, but I accept that many do and arguments about economics won't do much to persuade these people. There is also a worry that liberal democracy would be less viable in a country made up of people with little attachment to liberty. Again, this is a separate argument to the one made above, and one that should be considered on its own merits, which I won't go into here.
Economics may not be the whole story, but it's not insignificant either. The immigration cap that the government wants to bring in is a case in point – if the government wants to argue that reducing immigrant numbers is worth making Britain marginally poorer I'd disagree, but it's not a ridiculous argument. But right now, they're not doing that. I want to see them making the argument honestly, on those terms, not based on voodoo economics that claims that Britain will get richer out of protectionism and reduced specialization of labour. We won't, and we're kidding ourselves if we think that immigration restrictions will make us rich.