The Jan 1920 date is interesting. This is the year of the first Kynoch cartridges to the Dutch for the “Vickers” Luger, but were actually intended for all the Dutch Luger pistols. The Dutch began acquiring Luger pistols from DWM before WWI. _n 1914 they had a draft contract for 400 more pistols from DWM but the contract was cancelled by DWM to meet German requirements. In early 1919, the Dutch needed more Luger pistols, but DWM could not make they because of the Versailles Treaty. Instead DWM delivered “unfinished” parts in the white to Vickers who finished them and assembled the pistols and sold them to the Dutch. DWM also provided the Dutch their ammunition into 1918, but when the War ended the Dutch had to find a new source of ammunition. It appears that the Dutch or Vickers approached Eley, probably in 1919 and the first Eley production was, as John Crump said, was in Jan 1920. It is likely this was in response to the Dutch requirement rather than for commercial sale. There is an early drawing by Eley which appears to be their proposal for 9mm Para ammo to Vickers, who was probably acting as the agent for the Dutch. This drawing is dated 26 Jan 1920 and probably represents the initial Eley production-probably qualification and test samples. If any ammunition was made with this headstamp is was made in limited quantities since none have been encountered.
The only Britishproduction ammunition apparently delivered was headstamped K 20. Deliveries to the Dutch in subsequent years used this same headstamp through 1923
There is however an earlier Eley drawing dated October 1919. which illustrates the cartridge pictured above.
Only one box is known for the cartridge pictured above:
And the packing date on the box is 29 November 1920.
There is no way of knowing whether the priority for production was for the Dutch contract, which was likely the largest requirement and likely the biggest immediate return, or the commercial market. In anycase, there is no evidence I know of that production using the Eley name continued past 1920.
Hope this helps!
Much of the information above is from the excellent book “The Dutch Luger” by Martins & de Vries.