Brexit isn't a battle against elites rather it can be correctly understood as a battle between elites, a battle for power. More specifically it's a battle between a more controlled and moderate version of capitalism as represented by the EU and an unfettered US style of radical free market capitalism as proposed by Hayek and his supporters on the outer fringes of the conservative party and radical and extreme right movements.
The Brexit movement has a very clear structure. It is financed by very rich extreme right wing businessmen who also have very large media interests and who share an extreme Thatcherite-Hayekian vision for the UK which involves the abolishing of much of UK employment law, most taxation and the privitisation of the entire state except the military. Much as a client would engage a barrister, they have, through their media interest procured the services of various professional journalists and commentators, notably Johnson and Gove, (there are numerous others,) who are paid to make the case for the UK leaving the EU. These people are top notch thinkers and speakers and have used a variety of means to sway the public in this matter, notably sovereignty, the plight of the working man (a typical fascistic strophe) and, most corrosively, immigration. But most of this is just very clever advertising and PR. The real goal of the top-dog Brexiteers is to unleash unfettered, no holds barred capitalism in the UK.
Sendoake responded to FWLaing:
Very good analysis, thank you. I might add to that: it might be good for the EU once the UK gets out. After all, the UK was the biggest advocate of unrestricted, uncontrolled capitalism in the EU. We might move towards something more moderate after Brexit.