So I have now completed the recovery of my old laptop harddrive. Which took a while.
That was achieved by the manic words:
rsync -avz /home/russ user@backuphost:/backup/
The lack of a / after russ means that it also creates a russ directory.
Setting up rsnapshot would have been cooler, but not necessary in this instance.
Will have to make sure that I set that up on the next one. Or set up rsync to run on logoff.