As an American, and correct me if I'm wrong, I think that the most common leftist positions on anti-EU movements is that some of them are legitimate while others rest on romanticized nationalism. For example, there is good reason to believe that the less successful countries of the EU are getting screwed with high interest loans from the IMF that they are forced to take to continue their EU membership, along with the fact that their poor performance keeps their currency cheap which allows more successful countries like Germany to export goods and make quite the profit.
So the Greek anti-EU movement enjoys support from the left, while the British anti- EU movement I would imagine that most leftists are either against or neutral towards.
“How in the hell could a man enjoy being awakened at 6:30 a.m. by an alarm clock, leap out of bed, dress, force-feed, shit, piss, brush teeth and hair, and fight traffic to get to a place where essentially you made lots of money for somebody else and were asked to be grateful for the opportunity to do so?” Charles Bukowski, Factotum
"In our glorious fight for civil rights, we must guard against being fooled by false slogans, as 'right-to-work.' It provides no 'rights' and no 'works.' Its purpose is to destroy labor unions and the freedom of collective bargaining... We demand this fraud be stopped." MLK
-fka Redbrother