I'd rather get to the bottom of it and understand what's going on... I don't like devices with built-in cells due to their very finite liftime; hence why I went with this product in the first placeI think I'd just get some more rechargeable batteries from somewhere like Argos or Screwfix or get some lights that you can recharge via the USB from Halfords etc.

Thanks - if I repeat the test to failure I'll do as you suggest; usually once they've cut out you can turn them on again for another few minutes before they die again; so this could be a good opportunity.Yes. Just before when it would normally cut out.
Thanks for that really informative postSo you have 0.95x2.62 = 2.5Wh available from the battery, and Moon claim 43hr battery life at 25 lumen for your lamp, so that suggests it's drawing 2.5/43 = 58mW, giving 25/0.058 = 430 lm/W.
Being as "The current state of the art is 150 lm/W" and "the LED industry is aiming for 250 lm/W, with 300 or so the likely theoretical limit" something doesn't sound quit right. Nevertheless, it's not as big discrepancy as you seem to be getting.
I think you need to define what your end point is (subjectively too dim or does it just cut out?), and measure the supply current, then these might be of some help:
Nickel Metal Hydride (NiMH) Handbook and Application Manual
Alkaline Manganese Dioxide Handbook and Application Manual
My charger complained that one of the cells out of my desk phone was faulty because I forgot them and let them discharge until one went into reverse, but I managed to recover it by putting it on a power supply and nuking it with an amp or so for a few seconds.
Measuring the battery on and off load, along with the current is useful, then you can calculate the source resistance.
If you know what the lamp draws that will do as your test load, especially as you already know it's lasting 3-4 hours.

Presumably the 2.62v value is that between fully-charged and cutoff voltage (at which the LED dies completely)? To be fair to Moon, their figures are for Alkalines which I think potentially have more capacity than NiMH; although I appreciate this might not account for the discrepencies you describe.
After some time spent like a lobotimised monkey trying to pilot a spacecraft, I think I've figured out the multimeter. I've run a couple of current draw tests with the meter in series between the (unconnected from each other) battery and the terminal it's supposed to connect to, with fully charged batteries:
Mode 1 / 12lm: 0.12A / 120mA / 0.34W at 2.85v
Mode 2 / 25lm: 0.25A / 250mA / 0.72W at 2.85v
Both of which appear to be 18lm/W, if I've done my sums right..
So, if we consider the mode 2 figures as that's the setting the batteries were tested on, this suggests that over the 3hrs from fully charged that the light remained illuimated, it consumed 3x0.25= 0.75Ah or around 79% of the two cell's rated value of 950mAh each..?
For the grown-ups in the room, does this seem correct and would it be fair to suggest that, given the published discharged characteristics of NiMH batteries (which seem to operate well down to 1.1-1.2v then fall off a cliff) the remaining, unaccounted-for 21% could remain in the cells after the regulator circuit in the light has already shut it off?
The anecdotal evidence (thanks @albion!) suggests that the cells might be inferior / knock-offs, however the figures above seem to suggest that they're probably behaving as they should and that the light is consuming a lot more power than it should..
So; who gets the exploding box of dog turds in the post - battery seller or light manufacturer?