Thank you, that was helpful. The critical passage is:
Converting a database
Access 97 or earlier format databases are converted into Access 2002-2003 format by default. If a database is converted to Access 2002 or Access 2003, the database can only be opened by Access 2002 or Access 2003. To convert an Access 97 or earlier database to Office Access 2007 ACCDB file format, you must first convert it to Access 2002, Access 2003, or Access 2000. You can then convert the database to Office Access 2007.
This certainly sounds like just what I want, in theory. Has anyone had experience of it in practice? I do not want to purchase 2007 until I am sure it will work. I rang a Microsoft help line and they told me it wasn't possible to do this.