Assuming the wires separate when you untwist the cord, get them at least 100mm apart from each other and use a volt-stick to detect which is the live.
Also, where the plug is attached, are the three inner pvc sheaths brown, blue and green/yellow?
If you Google ‘volt stick’ you will find many. I don’t know if there’s one at SLMS, but there are at least two electricians regularly there who probably own them.
Otherwise I have one I can bring in tomorrow (Friday), or from Sunday onwards.
The other option would be to (with the lamp not plugged in!) use a multi meter and continuity test between the live pin and poke a needle into each wire at a time, technically leaves a pin hole in the insulation though