I don't think you'll find anything in BS7671 or it's OSG's. Though you'll not find a similar example being put forward as being compliant. Examples in the relevant OSG, will always be shown as separate electrodes being required!! So you could try actually showing the client these diagrams to explain what is generally required in such circumstances. lol!!
It's not too dissimilar to an old DNO supply that feeds 2 houses via a single TN-S cable looped between them, when you think about it!!.
In this case, commonsense would tell you to provide separate TT systems, for two completely separate supplies though. As wirepuller states, why anyone would scrimp on a simple earthing arrangement given the overall costs on converting these barns is beyond me. I put the blame squarely on the electrician responsible for wiring these two barn conversions. Even if both buildings were fed from a single supply point, having just a single electrode for both buildings would still make little to no sense. Another case of relying on RCDs and the single electrode TT acting only as a reference earth!! ...What's the betting it's a twig electrode too?? lol!!