Register ?
There's a fairly modern scheme in England called the Portable Antiquities Scheme - every region has an officer to record the multitude of small archaeological discoveries - and this person is yours:
Katie Hinds
Finds Liaison Officer
Salisbury & South Wiltshire Museum, The King's House, 65 The Close, Salisbury, Wilts. SP1 2EN
Everything recognisably antique - that doesn't need a wheelbarrow to move - should go through them. It takes ten minutes and two photographs of the object. The landowner should know about it too as he will have a very good claim for ownership.
My understanding of the process of getting a monument listed by E. H. is to initially include it in the county Sites and Monument Register - that needs some contact with Dr FitzPatrick's office - and then they propose to E. H. that it becomes scheduled. My experience is that the second part is fraught with politics and expediency.
With hindsight I suspect that the important recent discovery in the Avebury landscape is actually this pair of lunar coordinates and how they fit into the landscape. On the strength of your threequarters of an hour on Monday morning I'm going to tell the moonwatchers that Avebury has begun lunar observations.