Thanks for the suggestion Oxiegen, I have added "port=3306" to the connection string, but no difference.
I have already added a user from the 'server administration' panel on the workbench, and have ticked the same boxes as when it was originally on the XP machine. I already had mysql installed on my dev laptop for testing, so I changed my connection string back to use the "127.0.0.1" IP address and this connects fine. I think that this proves that my VB Net coding is correct, and that my connection string is correct. It therefore points to the Ubuntu server as being the problem, so I did a bit more testing: if I remove the user from the Ubuntu server, (workbench, server administration, security, users and privileges - remove) and try to connect I still get the same message (i.e. Unable to connect to any of the specified MySQL hosts.) I don't get any username / password errors. Does this have any relevance?