Immigration has no significant impact on wages.  It causes some increases and some decreases, but in either direction, the effects are small.

An increase in the number of migrants corresponding to 1% of the UK-born working-age population results in an increase in average wages of 0.1 to 0.3%.

However, there are some losers: each 1% increase in the share of migrants in the UK-born working age population leads to a 0.6% decline in the wages of the 5% lowest paid workers (whilst also leading to an increase in the wages of higher paid workers.)

This subset of losers (the 5% lowest paid) tend themselves to be migrants already working in the UK.

Source: Migration Observatory, Oxford

Immigrants are cleverer than us.

UK natives with a university degree: 24%.

European immigrants with a university degree: 35%.

Non-European immigrants with a university degree: 41%

University College, London. Nov 2014
(2011 data)