Hi Sue, 

Thanks for your response.
Looking back over my scripts to do the failover from one to the other, I did run the two SP's "sp_change_log_shipping_primary_database" and...

So, after reading a few more articles I found that the way to do it was to remove any references to the old entries in the following tables

[MSDB].[dbo].[log_shipping_monitor_secondary]...