That's not necessarily correct. That's only the case in a vacuum, it falls apart in reality.
For example, the US has routine shortages of farm field workers, in places like California, for picking etc. The wages are very low. It's a combination of nobody but illegal immigrants wanting to do the job for $10 / hour because it's a miserable job, and the business owner not being able to afford dramatically higher wages. It's a very persistent problem throughout California. In your theory, the wages could only be so low due to a vast over-supply of labor; there are in fact many other reasons an imbalance like that can occur.
http://www.sandiegouniontribune.com/news/2015/oct/25/decline...
http://www.wsj.com/articles/on-u-s-farms-fewer-hands-for-the...
http://www.nytimes.com/2014/03/30/us/california-farmers-shor...
The situation is somewhat complicated by the seasonal nature of the work, which means yearly cycles of hiring and firing. We normally associate periods of intense hiring with a shortage (ie, a recent shift in the economy means much more demand for some category of worker and not enough people have been trained yet to fill the demand), but in the case of agricultural work, that's part of the economy in steady-state.
I can go pick my own strawberries in New England when they are in season for $1-2 a pound. That season might only be about three or four weeks in June/July, but there's other stuff the other eleven months of the year. If I want fresh strawberries in December, they ought to be at a premium.
We used to use a lot of teen-aged labor for this kind of low-skill seasonal work, and I don't necessarily think there's anything wrong with that. There's still parts of Aroostook county in Maine where they have a weird school year, because traditionally they needed every warm body to get the potato harvest picked in early fall.
"Metcalfe says there will be temporary exceptions for people with skills such as nursing, because there is a shortage in the U.K."
Presumably central government has perfect information about the job market and will be able to make all the exceptions required in every industry?