Sorry long post, but much rather explain clearly what happened when I tried changing 12v halogens to 12v LED lights for a mate.
When I did my mate's change over to LED lights, it wasn't a question of swapping them over, because with his old SMPS (electronic transformers) that ran his 20W halogen bulbs quite happily, and he had one per halogen light, so in all he had 8 such SMPS and one for each Halogen.
So when he swapped halogen with LED, it started to flicker, that is when I came into the scene, as he called me over to find out why they are doing it, at first I had no idea as I was not into LED lighting, so I advised him to go back to the shop where he bought them from and and ask them why those LED lights won't run smooth on his old SMPS.
The shop man told him that he could sell him two Powertran brand SMPS and it could run 4 LEd lights easily as it is rated at 20-60 VA.
Strangely I did not notice until now, that this Powertran SMPS is Dimmable apparently, says on it, but doesn't have a separate control input for dimming as I saw on one other thread on here that some dimmable ones require 0-10v for dimming.
This one has no control input for dimming, so I am assuming it would dim on normal tungsten bulb type dimmers using SCRs.
Any way, I removed all his old SMPS, first from one row of 4 lights, and reconnected his wiring in parallel and where the mains 230v came in I wired the new SMPS, and connected its output to all 4 lamp holders, and then as we went about plugging one LED bulb at a time, there was no flickering at first, so by the time we had plugged 3 LED lights in, we could not plug the 4th one in because we had mislaid it and could not find it, so we left 3 connected and running with no flicker,
Next day I went back in and my mate got 4 more for the second row, and I went about doing the same to the second row what I did to the first row, removed his old SMPS, and discarded them, and rearranged wiring in parallel to run on another new single Powertran SMPS.
He also bought an extra LED bulb as we had mislaid one, so as we finished rewiring the second row, and inserted all new 4 LED lights in second row, and when we turned power on, they started to flicker, all 4 flickering in row 2, and then we switched on row 1 that had 3 LED bulbs, and it ran fine, no flickering, then we added the 4th bulb in row 1 and switched all 4 new LEDs in row 1 and they started to flicker as well, and quite badly so, then we removed the 4th LED bulb we added, so leaving 3 in Row 1, and now they were still flickering, something strange was going on and we could not explain logically,
this is when I started to check for 12v on ROW 1, and the voltage was all over fluctuating between 3.6v to 11v something, and the same thing was happening in row two, all 8 LEDs On and bad flickering, One LED even started to flicker like a disco light flashing ON and OFF.
This is when I suggested to my mate that I think we need proper wire wound transformer, and then he said wait I might have a couple, this is when he brought two black potted transformer same as OP's and weighed really heavy so there was no question it was a wire wound transformer but nicely build and all potted into a plastic housing with two set of terminals at either end, primary and secondary clearly marked as 240V and 12v
I swapped these and all went brilliant and stable.
Your SMPS Transformer cannot be said to not work, I would try it first before deciding to take the WW route, if iot works on your LEDs then you don't have to buy expensive and heavy wire wound.
and remember my mate's LED bulbs have a compensating circuit build into them that will provide a steady light at a wide variation of input voltage, but if the SMPS cannot meet the required current demand by 4 LED bulbs then it will start going into a vicious flickering cycle.
All I can say is let us hope these electronic SMPS can run many other brands of 12v LED bulbs, otherwise you are better off not buying 12v LEDs but go for 230V LED bulbs and do away altogether with SMPS.