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We might be at crossed purposes most lamps are plugged into a 13amp socket not a 5amp lighting socket. That's why we are discussing the fuse rating of that 13amp plug.
If you are talking about the 5amp unfused plug that fits the specialised socket then yes it does need to have cable rated for 5amp (or 6 I guess since the cu will very likely have a 6amp breaker).
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I thought we were talking about the fuse to put in the ceiling lamp that moocher wants to plug in and what is an appropriate value for that. Since it is a ceiling lamp that is designed to be hardwired I assume it has a 6A rated flex, or maybe 5A if it is very old (but it probably isn't very old by the look of the sticker).
Apparently you can buy 0.5 mm^2 2-core braided textile covered flex for the retro look. I'd like to think it isn't generally supplied with pendant lamps but perhaps it is with warnings stuck on it that are quickly discarded?
My understanding is that as the light fitting cable is only protected by the fuse/breaker in the CU it should be rated for 6A. I presume there is a BS/EN standard that light fittings need to meet that would detail that kind of thing?