Unfortunately I am not near a copy of BS7671 and won't be for some days. However I note the following from books referencing these regulations:
Bradley, J. 2009, 'A Practical Guide to the Wiring Regulations', Wiley, P131; 'When considering current-carrying capacity and the correction factors for grouping of a paralleled conductor circuit, each conductor should be regarded as a 'circuit'.
and
Locke, D. 2008, 'Guide to the wiring regulations (BS7671:2008)', Wiley, P73; 'It should be noted that grouping factors are applicable to parallel cables.'
Having read the old thread, there were a number of arguments put forward that while correct in themselves, did not prove or disprove the need for derating. For example, one contributor mentioned the lack of requirement to derate two grouped legs of an RFC. There is a perfectly good explanation for this because the RFC is a special case: The Iz of each leg is mandated by the regulations to have an Iz > In/2, due to the likelihood of unequal current sharing (otherwise, it would be acceptable to use 2x 1.5 T+E for an RFC). Since it is therefore impossible to load both legs to Iz at once, the grouping factor is automatically applied. Another argument concerned temperature rise of two adjacent hot bodies not giving rise to a higher temperature. This was irrelevant because it referenced sources of constant temperature, not constant heat input. There were other arguments and claims put forward one way or another that didn't correctly deal with the question in hand.
What I would like to see is an argument, based on sound physics, that grouped parallel cables comprising one circuit may be allowed to carry significantly more current than those of separate circuits, all other factors being identical.