Hold fire I think I've sorted it using MySql Workbench
Opened old server connection Exported schema dbname Created new connection to new server and MySQL Imported schema dbname and chose option 'New Schema'
Yes it went painlessly enough, quite easy to do as long as you remember to click the option to create a new schema when importing for the first time rather than overwrite the previous database you imported
I had one issue with one database but again easy enough to resolve by exporting the database first as separate tables, creating a new schema when importing the first table, then adding a table at a time to that schema until the one causing the error flagged up. Quick'ish fix and soon sorted