Rubus vigoi? I’m not sure if the diagnoses based on a young plant (as this one) are valid.

But here are some features of R. vigoi according to Flora Iberica:

1. Generally glabrous stems;
2. Prickles 5-9(12) per 5cm;
3. Prickle length: 6-8mm;
4. Prickle base width: (4.5)5-7(8)mm;

5. Leaf: upper surface glabrous or subglabrous (0-10 hairs per square centimeter; lower surface tomentose with single hairs;
   ….

What am I looking at???

I come to the conclusion that they are R. radula because I can’t find other possibilities. It’s true that these plants sometimes have smaller spines that remind me of the series Hystrix just as R. carpetanus that grows not far from here. But R. radula can also have them (9th photo is of a older stem so it is NOT to be considered as valid part for identification. It’s here just for illustrating the feature that may have been ignored). But the leaflet form is that of R. radula in my opinion.

The number of spines per 5cm also seems too many for R. radula if we only stick to Flora Iberica where it is described to have (4)6-9 spines. However, according to the German site http://www.rubus-sh.de/radula/verschiedenes.html: spines per 5cm on the first year stem of R. radula range from 5 to 11(16)!!!!

On the other hand, Flora Ibérica also mentioned forms that have abundant “pricklets” (smaller sized spines) on the first year stems — just as the website shows in some of the photos…

There is, somehow, another element that was described as “R. patientis” Monasterio-Huelin (1992) of the series Hystrix from more or less the same area. The name “R. patientis” is however an unresolved name which is not recognized by almost any parts. From one only silhouette of a collected specimen in the work “Revisión Taxonómica del Género Rubus L. (Rosaceae) en la Península Ibérica e Islas Baleares” (Monasterio-Huelin, 1992), R. patientis maybe is in fact the R. carpetanus that we know today mainly because of the similar leaflet shape which is distinct from that of these plants I saw.

Conclusion:
R. radula is the “reasonable” identification that I can give considering the terminal leaflet form and with help of some other sources of information on the number of prickles/pricklets.