WiFi functions poorly

Have installed Netrunner Frontier on a Lenovo Thinkpad Edge E145. The WiFi hardware in this laptop is a Broadcom BCM43228 module. The Broadcom driver installed is bcmwl-kernel-source
When starting up the laptop wireless activates properly but when checking the download speed it is far too low, like 2.3 Mbps instead of around 30 Mbps. The upload speed is mostly normal around 2.8 Mbps.
Switching wireless of and switching it on again mostly helps to get normal download speeds but the speed fluctuates quite a lot. Have switched Power Management off permanently.
When running Puppy Linux from a USB stick wireless functions normal, the download speed is always around 30 Mbps with little fluctuations.
My conclusions are that the hardware must be OK and the problem is software related.
Any ideas on how to fix it?
Thanks in advance for any suggestions.

If I am informed correctly you can also try another driver on this chipset.
So please try this and see if it works better for

# Remove current driver
sudo apt-get remove bcmwl-kernel-source
# Install binary blobs from the manufacturer
sudo apt-get install firmware-b43-installer b43-fwcutter

After that please reboot for changes to take effect.

Have tried your suggestion but the result is no wireless at all.
Will install the bcmwl-kernel-source again to have some wireless.