Gloster Gauntlet K4081

[AndyMa]

According to my first edition K serials book, Gauntlet K4081 crashed 8.36 with the A&AEE.
ASN agrees, adding an exact date of 31 Aug 36: https://aviation-safety.net/wikibase/68789
The individual history document at: http://mmpbooks.biz/gauntlet/AppendixGauntlet.pdf
says:
"K4081 • To Director of Technical Development at Glosters, 01/01/35 (Fitted with wheel spats) • Aeroplane & Armament Experimental
Establishment for type trials, 08/01/35 • To Bristols to fit Mercury VI, 24/05/35 • Glosters, 21/07/35 • Aeroplane & Armament
Experimental Establishment, 22/08/35 • Glosters, 14/10/35 • Crashed while with Glosters, 08/36 • Wreck to Aeroplane &
Armament Experimental Establishment, 15/07/36 • 187.40 hours"
(there is an incorrect date here, the wreck apparently went to A&AEE before the crash!)

However, K4081 is also said to have been supplied to the Danish Army in April 1936 as a pattern aircraft for license production, receiving serial J-21. See the Gauntlet page at:
http://www.milfly.dk/?page_id=1718
An article in Small Air Forces Observer 117 also says that K4081 went to Denmark. There is a photo of a very complete J-21 in that issue.

Can anyone clarify the true situation please? At a guess, one of the dates quoted is wrong. I did originally think the date of supply to Denmark could be wrong, but given that license-built aircraft were being delivered from September 1936 there wouldn't have been any point in delivering it much later.
Discussion on the Air Britain forum indicates that Denmark acquired one "pattern" aircraft before starting license production.
So was it an ex RAF aircraft, or a "spare fuselage" that was supplied?
If it was an ex RAF aircraft, there don't seem to be many candidates. Aside from K4081, we seem to have (thanks to Stig Jarlevik for some background work):
K4082 said to have become 867M on 20 June 1936 (thus perhaps a bit unlikely?)
K4092 damaged 8 Nov 1935 and SOC 2 Dec 1935
K4099 overturned at Duxford 6 March 1936 and SOC 2 May 1936
C/n 345 is often quoted as an identity, but I have no clue as to the origin of this.

Any further input appreciated!