I'm not 100% sure what rating method is appropriate for cables loose inside a hollow wall without thermal insulation, the descriptions I can find online of the installation methods don't seem to cover that case. ...
As you say, and seemingly rather strangely, this (which must be a very common method of cable installation) does not appear to be covered by any of the 'installation Methods' described in BS7671. However, although I may be wrong, I get the impression that most people consider this to be Method C. In fact, it would not surprise me if some people considered it to be 'in free air' (particularly if the 'hollow wall' were quite 'wide'), in which case the CCC of 1.5mm² cable would be 22A.
You can't totally protect idiots from their own stupidity. .... But equally i'm not convinced it is reasonable to expect people to notice that a particular cable is one size down from the rest of the circuit. One size step is only about a 1.2x change in core diameter! ...
I wouldn't argue with that, but, in this case, I'm not sure what sort of future idiocy/stupidity (or even just 'errors') we are contemplating ...
- All we know is that the OP was talking about ~15cm of 1.5mm² cable installed "behind a plasterboard wall" and protected by a 20A breaker. We don't know what sort of circuit is is, or what cable the rest of the circuit uses.
- If the cable in question were an unfused spur from a ring final circuit (seemingly very unlikley, given the 20A OPD), then any 'non-idiot' working on the installation in the future should understand they they could not 'extend' the circuit further from that spur, regardless of what size cable it uses.
- If it is a 20A (1.5mm² or 2.5mm²) radial circuit then, then there would be no problem with extending the circuit with (Method C) 1.5mm² cable, regardless of what size cable it is being 'extended from'.
What other scenarios are we considering in which people could be misled into doing something wrong in the future if (about six inches of) 1.5mm² cable were used for this socket?
... and even if they do notice it is one size down how will they know what installation method applies to it.
Given that the cable is apparently only about six inches long, I would imagine that the 'installation method' would be pretty obvious. However, even if it were much longer, I don't think that any future worker would have any (non-destructive) option but to 'assume' (hope!) that the installation method was such that it was adequately protected by the 20A OPD. Let's face it, even if it were 2.5mm² cable (which 'disappeared into a wall'), one could not be certain that it was not, say, Method 103 along at least some of its length and hence inadequately protected by the 20A OPD - in practice (unless there were very detailed documentation, which would be very rare), one could presumably do nothing but 'assume' that it (and/or the circuit's OPD) had been installed 'correctly'.
In any event, the above uncertainties would relate to the then-already-existing wiring. As above, if (as I assume) it is a radial circuit, then there would be no problem (aas far as the new wiring were concerned) in extending the circuit with (Method C) 1.5mm² cable, would there?
Thus IMO unless one is prepared to create and maintain proper comprehensive documentation and somehow ensure that said documentation is maintained long into the future one should try and perform their installation work in a way that is as conventional and error-resistant as possible.
I totally agree but, as above, unless I'm missing something (which is far from impossible), I'm not sure that the actual situation we are talking about (per OP) is appreciably "non-error-resistant". Am I missing something?
Kind Regards, John