I'm a bit curious about how you're being undercut in the labor market and simultaneously being priced out of the housing market. You seem to be implying that uncontrolled immigrants are earning less money, but buying more expensive homes.
EU nationals come to the UK, and they participate in both the labour and housing markets.
A small number act to stimulate supply in those markets (e.g. entrepreneurs setting up businesses, or construction workers building the pitiful number of new homes that get built each year), but the vast majority simply add to the demand-side, driving down wages and increasing rents and property prices.
This applies to both skilled and unskilled migrants. The former often come with savings and significant professional experience. Great for businesses, rubbish for our young people.
