At risk of being seen as repetitive
Good thread idea.
But before launching into any prescriptions for organised agitation, it's worth remembering the 3rd element of the leftist 'tryptich'; educate!
If we are going to effect any meaningful (supported) influence upon the direction of Brexit, I'm convinced that 'the left' needs to mount a concerted effort to analyse, explain and expose the motivations of those forces that have driven the process.
For my own 2p-worth, I'm convinced that Brexiteers on the right have been working to an oligarch-friendly, neoliberal agenda. Their real antipathy to the EU has never been the 'common market' aspects of the project, but it's aspiration to fiscal/legal political convergence under supra-state jurisdiction. The growth of such a power bloc was/is a genuine threat to global neoliberal processes of accumulation and (crucially) wealth defence based upon tax dodging.
Hidden beneath layers of nationalist, sovereignty guff the Atlanticist neoliberals of the (long) 'Brexit' campaign have worked to hinder, slow, undermine and ultimately destroy the development of a supra-state with the potential to interfere with the evolution of advanced neoliberalism as determined by the oligarcic class. Mere nations have no chance of challenging globalised capital or co-ordinating any response matching that of the super-state.
As such I am in agreement with those who feel that many were duped by the Brexit campaign, but more importantly such hegemonic distortion is going to make the challenge of turning around opinion very difficult.
So, sorry...no great ideas, but a suggestion that one line of attack has to be 'education'.