I have seen red 13 amp plugs clearly marked NHS which do not have fuses, but that is the only time I have seen it were there is no overload protection, and they are only fitted to machines where failure would mean loss of life.
Calculations for volt drop use design current, so for example the standard for a ring final is to consider 20 amp drawn at centre of ring, and 12 amp even spaced, so for volt drop we use 26 amp not 32 amp but it is still 32 amp for over load protection.
Years ago, about 1974 to 80 I was involved with entertainment and lighting. I managed to obtain a license to use type approved unfused 13A plugs which had to be protected within 1m by a 13A fuse or 15A MCB. The plugs were made to a high quality and in reality the only way of getting them was as a manufactured unit with plug, 1m 2.5mm² flex and enclosure with 15A MCB and reyrole, 15A 546 or couple of 13A socket in exchange for part of the license document, ie only one per license. Then we discovered the Xray plug [which was orange in those days] and marked "XRAY MACHINE" nice chunky plugs with terrific grip to pull it out but hard to obtain without being in the know.