Hat-tip to @Rhizowen for the below scientific answer, which helps explain the change in colour on the leaves from green to red (assuming some kind of disease isn't the cause):
Red anthocyanin pigments protect chlorophyll from breaking down, maximising the leaf's ability to produce and transport sugars -- so a stressed plant realising it's in trouble, tries to get its leaves to produce as much sugar as possible before they die...
Apart from those few leaves (about 5 to 10 in total), the rest of the plant appears to look healthy to me, from the little I can see from those couple of photos. Please correct me if I'm wrong on that observation, statement.
Below quote comes from Growing Small Fruits for the Home Garden:
Lack of supplemental watering from June to August severely limits successful production of blueberries in the Pacific Northwest. Shallow-rooted plants require close attention to maintain a uniformly moist environment around their base. They require 1, or possibly 2 inches of water each week, in the absence of any rainfall. Be sure the entire root zone is wet after an irrigation. Drought symptoms include reddened foliage, weak, thin shoots, and reduced fruit set. Maintain a 2-inch mulch layer to preserve soil moisture. A drip system, set on a timer, works especially well in keeping soil moist on a daily basis. Keep watering the plants through August to ensure good fruit bud development for the following season's crop.
I realise the above refers to Blueberries & not Blackberries, but the symptoms(s) look the same to me...
Take a listen of this, Effects of Drought and Drowning on Plants, then let us know what you think... I'm currently thinking it's water related, either not enough or too much.
Also try this tool, The Berry Diagnostic Tool, and see what you can come up with. Personally I couldn't find anything that resembles the symptoms shown in your couple of photos.
The gardening "experts" on twitter don't believe it's a disease, most are thinking drought related and the plant should be fine if well looked after this Autumn eg
Put down a 2inch (50mm) thick layer of compost on top of the soil, will provide a slow natural feed.
Ensure the plant gets the correct amount of water.
Good luck! and please let us know how the plant gets on.