"Wait, sorry, is it the unskilled or the over-skilled natives who suffer because of immigrants?"
I am sorry I have not made myself clear. I agree I have been a bit ambigous. We have people with utterly useless degrees who do not have USEFUL vocational skills. We also have people with no qualifications whatsoever for whatever reason. Both groups find it hard to find work. Young people with skills often find hard to get a foot in the door due to lack of experience.
The reality is that immigration opens up a high quality pool of potential employees. This is good for the British ecomony in many ways, but not good for natives who cannot compete against better quality applicants.
"But National Minimum Wage creates a floor to how far wages can be suppressed - by immigration or any other cause. It's one of the reasons NMW is so important: it prevents exactly the scenario you're describing."
Why do we have whole raft of in work benefits to support those in work if the NMW is enough? There are even tax credits for single people on a very low wage and housing benefit.
I don't think that national minimum wage is high enough. Employers are also able to get around this by insisting that cleaners or people who work in the building trade are "self employed". There are also employers who illegally pay cash in hand.