I had similar issue with this for BCM4352 and been compiling drivers for each new kernel. Until one day, I've found out that in "Software & Updates" you have magical tab "Additional drivers". Just select alternative, proprietary drivers and you should be fine.
In case above doesn't give anything to choose from, here's manual way to make it working. Drivers I used were downloaded from here: http://www.broadcom.com/support/802.11/linux_sta.php - but it seems it's no longer there.
Most probably, you can use the newest one available here: https://www.broadcom.com/support/802.11 - then choose 64-bit version (https://www.broadcom.com/docs/linux_sta/hybrid-v35_64-nodebug-pcoem-6_30_223_271.tar.gz) or 32-bit version (https://www.broadcom.com/docs/linux_sta/hybrid-v35-nodebug-pcoem-6_30_223_271.tar.gz).
You can also go for drivers that I've used, thanks to Wayback Machine (Internet archive) - https://web.archive.org/web/20141213071440/http://www.broadcom.com/support/802.11/linux_sta.php - links on this website point to the exact drivers (version) that I've used. Links for both: 64-bit and 32-bit are working.
Download, extract and follow the readme file precisely. In a nutshell, something like this should be enough:
start by opening terminal and get required packages for building drivers locally:
apt-get install build-essential linux-headers-generic
apt-get build-dep linux
Navigate to the directory with extracted content and execute:
make clean
If this is the first time you install this driver, please make sure to follow all 3 bullets in section "INSTALL INSTRUCTIONS - Fresh installation" that is:
1: Remove any other drivers for the Broadcom wireless device.
2: Insmod the driver.
3: Setup to always load at boot time.
remeber, this are only headings, well explained in readme file. I'm writing to follow this explicitly, as initially I just removed other BCM drivers and "insmod-ed" this one, but I had to insmod it after each reboot. This third section (3: Setup to always load at boot time) is easy to miss.
Hope this works for you as well!