How to configure preferred network for internet?

I am connected to a LAN network and wireless network. Both provide access to internet.

Sometimes when the internet on LAN is not working, the browser simply throws an exception instead of switching to Wireless. (Wireless is on and local peer computers on wireless are connectible).

Apparently it is giving more priority to LAN. How do I increase the priority of Wireless or set it as an automatic fall back?

Go to system settings -> Network -> wired

Then click on options, select IPV4 tab, and click on routes.

Finally enable the Use this connection only for resources of its network

This way Ubuntu will use only Wireless for accessing the Internet

It's not the browser's fault. Routing is done by the kernel as configured by NetworkManager.

NetworkManager only monitors the local link in deciding whether or not to enable a connection, and it always prioritizes wired over wireless. It doesn't monitor whether "the Internet" is reachable via connections.

To force NM not to use the wired connection (because it is connected to a malfunctioning router) open the Connection Editor via the indicator and delete it from the list. Or unplug the Ethernet cable.