So to answer your question: Ubuntu will let you access the next web, and Android probably won't.
If you're talking about developing some brand new means of worldwide communications, this seems extremely improbable if done by the 1% of the rest of us (basically, hobbyists and techy people). The internet required tens of billions of dollars worth of development and infrastructure to get to this point, how will it ever happen without the sponsorship of large centralized entities?
If you're talking about leeching off the existing internet infrastructure to communicate with some brand new protocols over them, who's going to let you do that? Both companies and governments would have incentive to put a stop to this in any way possible, because it drives away customers from the manufacturers and signers of all "secure" devices and lessens the amount/value of surveilled data. It may be allowed at a small scale, but I'm not seeing how anything long-term could be established that could threaten the existing powers in any way.