I had the same issue with 12.10 on my macbook pro 11.3 I found the correct driver package off ubuntu website, while in OSX, and put it on a usb, then rebooted in ubuntu with rEFInd, put it on my desk top, purged the old with:
sudo apt-get purge bcmwl-kernel-source
//then:
cd ~/Desktop
sudo dpkg -i *.deb
sudo modprobe wl
sudo apt-get update
sudo apt-get install bcmwl-kernel-source
sudo apt-get update
Then went into update manager it ran through some changes then into setting to see the driver then correctly displayed clicked on it hit apply, restarted and it worked like a dream. Here I'll upgrade myself real quick and see if I can get it working in 16.04 as-well I love fixing broke things.
/And yes I know I went into overkill with update, but once more wifi from
phone, kept loosing signal and didn't want to miss anything./
Yes, just updated myself, same process, you can find the correct packages in your install disk by mounting it from any other os you downloaded it on, or usb you hooked up to load it, and search for the bcmwl package grab the box and drag it onto your desktop then do the commands above, you will also need dkms, you can find either when the disk is mounted and your are viewing the files in the seach bar, then
cd ~/Desktop
sudo dpkg -i *.deb
sudo modprobe wl
sudo apt-get update