I can certainly see where the authors of the guidance were coming from. A double socket is IMO less likely to see two large loads than two single sockets in distinct locations and on a 20A cable two large loads could easily be an overload.
I don't doubt that such was probably their thinking, but they are just guessing/assuming, which is never a very good idea! Given what
could be plugged into a double socket, if they believed that 26A would be too much, their 'guidance' should surely have been that only one single socket was 'acceptable', shouldn't it?
More to the point, they appear to be 'guiding' people to do something which, taken together with 433.1.204, might well cause people to do something which appears to be actually contrary to the regulations (433.1.1).
I can't tell you whether this was intended, but 433.1.204 can be easily read to be saying that the CCC of the cable forming an unfused spur from a ring final may be as low as 20A (e.g. 2.5mm² Method A, if one uses Table 4D5). If one has such a cable, and followed the guidance that it was OK for it to feed a double socket, then one would have a length of cable with a CCC of 20A which had 32A upstream over-current protection and 2 x 13A (i.e. 26A) downstream over-current protection - and I can't see why this would not violate 433.1.1.
In that case, guesses/assumptions are not required, because it's all about the ratings of the OPDs, not the guessed loading - i.e. although, given certain conditions, downstream over-current protection is acceptable to BS7671, 26A of downstream protection of a cable with a CCC of 20A is definitely
not acceptable.
In terms of what is permissible for an unfused spur, one really has to rely on (comply with) 433.1.1 (and not the guidance of Appendix 15), since 433.1.204 itself says absolutely nothing specific (other than 'unfused spurs' are allowed from ring finals) - so could be read to be suggesting than an unlimited number of sockets could be supplied by an unfused spur.
P.S. The OP never said the outside socket was a single.
Yes, I noticed that. However, I felt that, should we discover it was a double, and given that we were told that it was only going to be used for very occasional vacuuming up of leaves, we could always suggest that it should be changed to a single!
Kind Regards, John