Thanks to all for the various comments and the detailed anecdotal information. My previous and only visit to the Royal Military Academy Sandhurst was in 1967 (54 years ago!) as member of the Combined Cadet Force!
The badges were acquired as part of a job lot of anodised badges so I have no provenance. They could have been painted by the previous owner/collector recently!
I have therefore revised the eBay description and consequently lowered the price! See:
https://www.ebay.co.uk/itm/194196225389
Tim