1. Don't do anything the state considers naughty. I suggest you kill yourslf now if you consider this viable.
2. Steal someone else's WiFi and deal with the moral consequences. You can do this by finding a "VendorA7E4B4" lookalike SSID (default configuration) and using the password calculator here: http://www.nickkusters.com/Services/SpeedTouch/Lookup - I only know of this as I had to lock my router down due to unauthorised access.
3. Use a VPN and risk being logged or falling foul of RIPA.
4. Use a dead drop http://deaddrops.com/ and risk being bagged at site.
5. Use SSH tunnels + proxy and risk misconfiguration + logging and RIPA.
6. Use paper or sneaker net and risk stop+search and RIPA.
Welcome to the machine.
To make something like that more user friendly though you could just install VPN software like OpenVPN on your VPS. This also ensures things like DNS queries are sent over the VPN so they can't be intercepted on their way to the server.
Of course this assumes you trust your VPS provider, at least more than your ISP.