Leftist plot?
You have to hand it to the Tabloids for convincing everyone that free-trade blocks are a left wing policy, but last time I looked the EU was about the free movement of trade, labour, goods, services and capital aka the bedrock of capitalism. It's a common error to think the left are in favour or bringing down barriers - they are not. They like regulation to protect workers.
New Labour have adopted Neo-Liberalism under Neil Kinnock and John Simith, as well as Mrs Thatcher. The difference is really the degree of regulation and types of regulation.
Sure, the EU doesn't respect national sovereignty, but as we've seen with the banks, nor do corporations.
This is why the Tories have had their knickers in a twist over the EU for years. On one hand, they love the market driven free trade economic blocks, that allow people to commute by 737 (not having a dig, just an observation that it seems the EU seems to rather help than hinder yourself)) but aren't so keen (being the party of the establishment) on trashing national boundaries. They obviously couldn't replace their market policies with protectionist left wing ones, which they have fought against for years, so they are stuck in this paradox.
Rather like the people the use low cost airlines and the internet, but only want to mix with their own kind.
PS I think you'll find both Bob Crow and the BNP are against neo-liberalism and the EU for two very different reasons.
PPS I have the same reservations about the EU as well because its not especially democratic and too centralist for my taste.