This is the Britain Stronger in Europe first campaign video:
As you can see, the basic argument for remaining within the EU is that the union has been wonderful for deregulation, cut-price travel, flogging wine and travelling abroad on your gap yah. So this is the state of play at the moment. The left critique of the EU says that it's a Europe of the neoliberal bourgeoisie, a Europe of spivs, business mercenaries and yuppies. Meanwhile, the major campaign for the EU defends it on the grounds that it's a Europe of the neoliberal bourgeoisie, a Europe of spivs, business mercenaries and yuppies.
Also note that it opens fire with a fairly obvious piece of racist dog-whistling. Far from there being the slightest progressive, internationalist content to the 'In' campaign, let alone anything remotely centre-left and solidaritous, it looks very much like the opening float in a carnival of reaction about to plough through British politics.