The British government published the official report on the impact of migration on unemployment among Brits. 

Earlier this week the government was accused by opposition MPs of deliberately withholding the report, which found that “there is relatively little evidence that immigration displaced Brits from their jobs in the periods of strong economy.”
The new analysis of the Migration Advisory Committee (MAC) found that there are “some shifts in the labour market during the recession.”

According to the report, however, the lack of sufficient evidence that the EU migrant workers take the jobs of the Brits, doesn't mean they don't have an impact in certain circumstances.