1) She proposed the idea, on briefing notes or in the speech, it doesn't really matter.
2) You missed the direct quote from May in the article? Her opinions are very clear on this and neatly mirror Trump's populist nationalism. To quote directly, she claims that British people are:
out of work or on lower wages because of low-skilled immigration
Given that employment is close to an all time low and most products bought are imported and thus nothing to do with low skilled immigrants this is clearly untrue. They may be out of work or on low wages due to globalisation, robotics, austerity, the markets, the dominance of china, the decline of British industry etc, but tying this to immigration is mendacious, dangerous, and entirely without basis in fact.
As robotics continues to take over, and most manual jobs disappear in the coming decades, this explanation of foreigners taking our jobs will become more and more appealing and more and more dangerous.