Wired internet connection is very slow on Ubuntu 16.04.03 LTS

Run in your terminal with correct ethernet port number you are using. Here I assumed it is 'eth0':

sudo /sbin/ethtool eth0

and see if the duplex mode is Half or Full. If it is Half duplex change it to full duplex with this command:

sudo /sbin/ethtool -s eth0 duplex full

You can also change the ethernet port to Half duplex with this command:

sudo /sbin/ethtool -s eth0 duplex half

However you need to install the ethtool first if it is not yet installed.

I have found the answer to my question...

It seems that I had the wrong DNS nameservers set up. My server has as nameservers the former IP address of the router and the current IP address of the router. While this worked perfectly well in the end, it seems it was slowing down finding the site, which made speedtest-cli time out during its 40 test downloads, producing a slow download speed.

The fix was to update the name server in */etc/network/interfaces* to 8.8.8.8 and bounce the network adapter and now the speed is the more normal 29Mbps.