Thanks for the detailed response, apologies, but some of the information wasn't clear to me at the start, we've just moved house so i just keep coming back to this when I can.Ever so slowly you are "leaking out" some of the information that you should have supplied in the first instance!
From that which you have written (so far) it is not clear that the "Power Supply" IS faulty", since you are reading Voltage
Reading the labels on the pictures (eventually) supplied, we now know (?) that you have "Hafele" Kickboard Strip LEDs - supplied from a 12 V AC (500 mA) TRANSFORMER via that which Hafele calls a "Master Junction Box" - rated at up-to 16 V AC, 500 mA.
(One might wonder if this "Master Junction Box" actually contains a "Bridge Rectifier" - given that it has a "rating"
AND
Polarized output connectors ! )
The "Strip LEDs" (how many?) may be connected via 2-Pin DIN connectors to the TEN sockets on this "Master Junction Box"
19 V (?) - on "No-Load" (?) - Where measured (?)
AC or DC (?)
You can plug one or more "Strip LEDs" into the "Master Junction Box" and measure the voltage supplied at one of the unused 2-Pin DIN sockets.
If you read 19V AC, the chances are that the supply is OK but there is "No-Load", indicating that the "Strip LED(s)" is/are Open Circuit. (Faulty)
If so, OBTAIN a (say) 150 Ohm/1 Watt resistor, insert its leads into a vacant 2-Pin DIN socket and check the voltage reading - on its leads.
(150 Ohms would represent about a 20% Load on the Transformer.)
You should then read around 12 V AC, if the supply is OK
- or 12V DC, if there IS a rectifier in the " Junction Box".
Wall wort was showing 19v when switched on at the wall and multimeter set to AC.
I am not at home at the moment but will get the junction box plugged in and powered up later and check voltage at an empty terminal.