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I would believe that most EU immigrants wouldn't get one. Having gone through the non-EU immigration system, I've seen the hurdles you need to cross become substantially higher in the decade that I've been here. Right now, the biggest barrier is the requirement for a non-EU migrant to earn a wage of £35000 per annum or above.
Had this rule been in place when I was finishing my PhD, I would have had to leave, rather than staying in the UK to post-doc. One of the post-docs in the lab I was in (Singaporean national, PhD from Cambridge) opted to do research at MSKCC in the US, rather than here, because she wouldn't clear the wage barrier on a post-doc salary.
Add to that the application fees are outrageously expensive (applying for indefinite leave to remain cost me £1800) and add to that the new NHS surcharge they have (an extra £1000 on top of the application fee for an American colleague of mine), then yeah, I do feel it's out of reach for many.
There was even a story on the Today program yesterday about how we can't get the curry chefs in this country anymore because of the £35000 wage requirement.
http://www.theguardian.com/politics/2016/may/27/leaving-eu-could-cause-catastrophic-worker-shortages
So Cameron suggests EU immigrants may need a VISA. 88% would not get one.
Fuckery. Or HamFace scare mongering. Dunno. I don't trust the Brexitters much tho.