The UK, with its relatively liberal immigration policies following recent enlargements, has been one of the main recipients of migrants from new EU member states. This paper poses the questions: what is the effect of immigration on a receiving economy such as the UK? Is the effect beneficial or adverse for growth? Does emigration have brain drain effects on sending economies? How differently would skilled (or unskilled) migration affect both receiving and sending economies? What factors would contribute to immigration/emigration benefits/costs and economic growth driven by migration? Who are the winners and losers in both the sending and host regions? We utilise a two-bloc endogenous growth model with labour mobility of different skill compositions to address these questions. We show that migration, in general, is beneficial to the receiving country and increases the world growth rate. With remittances, the sending country in aggregate can also benefit. The only exception is in the case of unskilled migration, which can actually have a detrimental impact on the world growth rate. This possibility however seems to be unlikely by our examination of migration trends. Winners are migrants, and the skill group in the region that sees its relative size decrease.