Hah! I'll give you that only if we get a "hard" Brexit - if we get a "soft" Brexit (or no Brexit!) - that is, keeping free movement in exchange for free market access, and thus having to live by all the rules but getting no voice in deciding them - then I'd couldn't really call that the masses having "a lot of power".
Remember, nothing is decided yet, so it's a bit early to crow about the power of the masses to do anything apart from cause the Pound to sink like a stone.
A "soft" Brexit would not result in us leaving the EU, not in any practical sense. We'd still be a member, all that would change is the type of member to more of an "associate" member than "full" member.
That could be spun as "leaving" the EU, but if we still have free movement, free market access, still have to abide by a large number of their rules, and still pay into various EU funds, have we really left?
Well, they got to win their referendum. As ipsi said, they may not in fact get to be out of the EU. There are plausible scenarios where that vote does not lead to Britain actually leaving.
I think the most interesting actions are those which organize. In a large democracy, organizing votes is magnitudes more interesting than voting itself, and it is on this organization game that I think the masses will lose, time and time again.
Signing petitions => will this translate to well-targeted get-out-to-vote drives for contentious districts?
Discussion on forums => will this translate to well-targeted get-out-to-vote drives for contentious districts?
Installing browser extensions and using Linux => will this translate to mass-market behavior?
Organization is the truly interesting game, and those in power have had their eye on the ball from the start. I also don't see how Brexit is a beacon of hope for collective action.
Brexit showed that democracies don't really deliberate things, and instead just vote Yea/Nay with 0 attempt for common consensus. Popular disagreement is democracy at its worst, especially when there are 0 effective deliberative processes, because it means a nearly maximally displeasurable voting outcome. In the case of Brexit, that meant that 48% of the nation is displeased. Brexit is absolutely not a lesson of grassroots power, or the kind of things small people can do against large powers.
* Use firefox/icecat * Install uBlock origin * Sign petitions on change.org * Participate in online discussions * Use GNU/Linux (trisquel is good)
etc...
If there's something that brexit taught me is that masses have a lot of power.