Britain has always had 'pure sovereignty'. With or without the EU, their parliament can do pretty much anything it wants (the US or Australian legislatures are quite limited), including leaving the EU.
Re: Austerity/neoliberalism, that's got very little to do with the EU and a lot to with Thatcher being elected in 1979, with the only non-Conservative government since then being Tony Blair - who wasn't exactly economically left wing.