Thankyou to you both.
I have tested the problem using 4 devices, 2 Samsung and 2 Google. That is with 4 different versions of Android and Gmail, 2 different Android Contacts lists and 2 Samsung Contacts lists.
It is Gmail that is the cause of the issue that I had.
I have changed the syncing between devices and Gmails. Unfortunately I did not keep a precise note of what I did.
The only suggestion that I can give to anyone else who has a problem with their contacts list is to try things with other devices; and see if Gmail is at the heart of the issue, if they are using an Android device.