The Brexit Campaign could have easily been defeated simply by a package of legitimate reforms to the EU, addressing the very valid concerns voters across the EU are expressing. But they are not interested in a reformed EU. They want the EU they have. Worse they want the more monstrous and smothering EU that they envision! And they have no intention of backing away from that goal.
Anything that's "free" is gonna be paid for by somebody. Now, the various EU member states will likely pool their money together to pay for this. The inevitable outcome, of course, is that richer EU member states will be footing most of the bill, and poorer EU member states will benefit disproportionately for what they paid.
The UK is a wealthy country, so it'd likely be among those that pay more than it would receive in benefits. The UK can pay for its own "free" Wi-Fi, and it'd likely be cheaper than for them to participate in this program as a EU member state.
There are some good things about Brexit and there are some bad things. When the economy in Greece was really bad, there were problems that came all the way over to the United Kingdom. Getting out of Brexit means that the United Kingdom can decide for themselves how they want to deal with social issues like free Wifi for everyone.
I find it laughable that anyone would consider Brexit to be a big mistake because the U.K. will not be getting free WiFi. It's the notion, and implementation, of all this free stuff that caused Brexit in the first place. When will people realize once and for all that government provided stuff for free is not free?
Just like the saying "there is no such thing as a free lunch," there is no such thing as free Wifi in the modern world. Such broad, all-encompassing programs that are implemented by ruling bodies always operate horribly inefficiently and are rife with money-grubbing individuals who exploit these inefficiencies for personal gain.