No, but saying £20 an hour is just being silly, but if locals aren't willing to work at some of the crappy jobs for NMW then the employers will have to raise wages to entice UK workers in. Even the reports that say immigration hasn't overall affected wages, do acknowledge there has been a small downward pressure on the low skilled manual labour end of the market, and this would be corrected if we didn't have the Eastern Europeans to do it.
This issue is forever misinterpreted. Not only for the last century there is always someone perpetually blamed for "stealing them jobs for pennies", whether it's Irish, various "illegals", Polish or Bulgarians, but also because there is a notion of some sort of cumulative evil exploiting employer figure who accumulates vast amount of cushy wealth between paying "them migrants sleeping ten a bed in shipping containers" pennies, and charging the customer a fortune. In real life free economy, outside of Socialist Worker articles and UKIP mythology, this doesn't happen. Unskilled and low skilled labour wages undertake constant adjustment on workforce supply basis - the days when bricky or road maintainer would break top tier in annual wage are over, because such wage discrepancy doesn't exist anywhere else in Europe. And it's not unfair adjustment, it benefits the economy.
In a scenario where you artificially cut off supply of labour to protect local market, the impact is not on the fatcat employer, but on consumer directly. If Polish builder is gone and British builder will not work for less than £150 a day, his benefit of higher wage is paid at the expense of hundreds of customers a year. So the question is - how much more are YOU willing to pay for your garden wall or your carpeting, how much are YOU willing to pay for Amazon delivery or pizza to your door, how much service charge are YOU willing to pay in restaurant to dish washers and bus boys for all unskilled and low skilled functions to be performed by someone born and bred on England's pleasant pastures and paid "decent wage"?