Watching the NZ Rugby Aotearoa I have been impressed by the idea that the various rivalries between clubs have led to inter club trophies. Not dissimilar to the 6N including the Calcutta Cup - its a side event that adds to the competition between England & Scotland.
Interclub rivalries within English rugby are generally those associated with proximity (Tigers v Saints, Bath v Glos for example) but they are rarely recognised beyond that. Historically our big rivalry was with Wasps because of our common origin.
Isn't it time, and appropriate, to mark that rivalry with a trophy? It could be the Hampstead Cup, The Tichener-Alford Shield or something similar. In essence a recognition of our two clubs linked history and a trophy to be held by the winning team after each competitive game in any competition.