If companies want cheap labour they can go anywhere in the world, but they don't. People come here to work or invest in a company, partly because of what Britain stands for; skills; lifestyle etc we are a desirable country for much more than our benefits sytem, and we always have been.
if they want access to the single market called the EU without import duties, they need to be in the EU.
What people want will be much worse for the average worker. People don't pay attention to the fact that companies can move, but want to restrict free movement. You are right that there are certain advantages to being the UK - skills, language etc, but at some point the fact that labour is cheaper in bulgaria will be a draw. Currently that draw isn't so big because those people can move here. But if they couldn't, it might be worth it to move there.
We won't suddenly have no one wanting to come here to work or companies relocating to Poland in droves
it may not be in droves. but expect some to go. Then, instead of some lower wage jobs here, all the jobs will go.