The long-term persistence of a species is closely related to free movement within the meta-population, and the meta-population with barriers to movement is more likely to go extinct than the meta-population enabling individuals to track resources as they fluctuate through time. It follows that larger meta-populations are more resilient to change than smaller meta-populations.
The analogy with human societies is obvious. The creation of large territorial blocs enabling free movement of people and resources (capital, goods, services) has demonstrably been good for regional "meta-populations" of humans, even if locally some populations might lose out in competition with newcomers.
Preventing "sources" from importing individuals from "sinks", and preventing "sinks" from exporting individuals to "sources" will depress the meta-population as a whole with the consequence that "sinks" will lean towards local extinction and "sources" will maintain populations below their carrying capacity. In the long term, and exposed to inevitable stochastic events, even "source" populations might face local extinctions.
Meta-populations in natural systems are not equivalent to meta-populations in social systems, though, because human societies are not linearly dependent on the amount of natural resources found locally. Wealth (fitness) is also related to innovation and entrepreneurship which, in turn attract, capital. But all of these factors are stimulated by competition (and its reverse cooperation), and both are boosted by free movement of individuals in large human meta-populations.
The irony for the UK is that the massive creation of new jobs that attracted massive numbers of new migrants from Europe and elsewhere, are a consequence of the success of an open economy within a large meta-population. Work towards a closer economy, and you will be able to reduce the inward fluxes of migrants not so much because of the effectiveness of the border controls but because the country will be generating fewer jobs and with fewer jobs less innovation and entrepreneurship and, as a consequence, less capital to create new jobs.