If the powers that be decide to cut internet access, they'll succeed, period. Any non complying ISP would be raided for acting against national security (insert political bullshit du jour here) etc. What common people can do (again: common people, do not expect any help from any corporate entities) is to create their own slow as hell Internet through mesh fault tolerant nodes that would arrange themselves automatically no matter where they are located, provided they have coverage, which would limit the global bandwidth to the bare minumum to exchange emails, small files and probably stuttering voice communication. Forget about streaming movies, online gaming and anything that requires speed and/or low latencies.
In case of real emergency however, you don't need any of the above; texting, email and slow upload of photos/videos would be more than enough, as it's extremely likely that they will become more important compared to anything else. Resurrecting USENET (like one micro server for every node) would be a nice touch since it requires a fraction of a fraction of the horsepower required to run any social network site.
As for the technical side, it will require higher power output than what it's usually employed by WiFi cards and access points. Nothing exceptional, Watts instead of milliwatts, still it would be illegal, as would be the use of external directional antennas to link static nodes from longer distances, so if they need an excuse to SWAT mommy's basement to turn off that Raspberry PI based node because it poses a security risk for the country, they'll have it.
Now, if I had to build it, I'd probably start from some mesh networking software on the smallest platform I could find that could sustain the traffic (there are better and cheaper boards than the Raspberries), then would provide the system with longer and shorter distance links by using multiple WiFi NICs. The best node is something that can run off solar or any non grid power and whose OS would rearrange the links with other nodes making seamless connections.
Here are a couple links on the subject of mesh links.
https://www.cwnp.com/wp-content/uploads/pdf/802.11s_mesh_net...
https://en.wikipedia.org/wiki/Wireless_mesh_network
In other words, it's doable to some extent, but be prepared to encounter resistance, jamming or worse.
Thinking globally, if the shit hits the fan, and i mean real shit, then one probably has to return to analog communications; in adverse conditions, a portable CW ransmitter with concealable "tactical" antenna would have a lot more chances to reach another continent than the greatest WiFi card to make to the next city.