Using the answer by @creack I did the following on my Ubuntu install to move my entire docker images/containers folder to a new location/disk. The great thing about doing this is that any new images that I install will then use the new disk location.
First stop the docker service:
sudo service docker stop
Then move the docker folder from the default location to your target location:
sudo mv /var/lib/docker /thenewlocation
Then edit the /etc/default/docker
file, inserting/amending the following line which provides the new location as an argument for the docker service:
DOCKER_OPTS="-g /thenewlocation/docker"
Restart the docker service:
sudo service docker start
This worked 100% for me - all my images remained in tact.