Why are people going off on splices in household power cables when the OP's question obviously is about a low-voltage repair on the secondary side of a power supply?
Seems things got way off course in my absence overnight! The cherry on top, 'victim blaming' me for it breaking in the first place.

Anyway I just managed to fix it.
I tried first with heating a small screwdriver and lighter which was a total fail. The lighter would not get it hot enough and I don't think it even made a dent in the solder.
Tried a couple of other metallic items to the same effect.
Next I tried with heatsink which was a success. Awkward, as I was trying to fix back a wire onto a corner terminal connection on a small pcb, but successful. I have used this same technique to make junctions on wires before. Messy but the result was a strong connection once the glue dried.
I snipped the heatshrink to make a rectangle and placed it over the corner with the wire underneath in place. I then lit it a bit, but not too much to make it overshrink and lose too much shape, then pressed down with finger. Repeat until a decent bond is made against the pcb. Gave a little wiggle and seems secure.
Dispite what the other user said about me being rough with it, I see the problem is the wires which I soldered are not held in place beyond the connection so any movement is going to put some force on the connection rather than if I say glued down the wires to the wood at the entry point to minimize the strain. It can also be because of my imperfect soldering skills, which I have done very little as usually I would be just attaching to ring connections and clamping and using heatshrink on the wire.