The recent problem with BCM4313 cards seems to be related to an upgraded version of the
bcmwl-kernel-source package. As a workaround, I suggest downgrading it to the previous version, by using the following steps.
sudo apt-get remove bcmwl-kernel-source to remove the package.
Install the older version
sudo apt-get install bcmwl-kernel-source=220.127.116.11+bdcom-0ubuntu6
Manual deb downloads are available from here: 32bit, 64bit. Install the downloaded file by double clicking.
and paste in the pollowing
Pin: version 18.104.22.168+bdcom*
PS: The workaround has been adapted from here. Unfortunately, I've no way of testing it, so please, let me know if it works, ... or not.