The trope of naked Celts (and, overall, Barbarians) was already quite famous and widespread in Antiquity and especially "naked fighting" both in text or artistics representations such as
Naked fighting was overall a fairly common heroic trope in the ancient Mediteranean world, including in ancient Greek art, and as we otherwise know that while lightly equipped, Greek did not went to battle in their birthday suits, we can wonder about what Hellenistic art ("Dying Gaul" and "Ludovisi Gaul" to convey especially as they were made for Hellenic viewers familiar with the themes displayed of heroic and pathetic nakedness.
The association of "fighting nudity" with ancient Celts, however, is also a litterary trope written down by the turn of the millenium but accounting for the wars against Galli/Galatai settled or raiding Italy, Balkans and in Anatolia, or employed as mercenaries in Carthaginian, Hellenistic or Roman armies; especially Diodorus Siculus^(1) (29-30) Livy (XXII, 46), Plutarch (Crassus, 25)^(3) and Polybius (II, 28)^(4). Reading these, however, brings some nuance.
Safe Polybus' every account describe a "gymnastic" nudity, that is further precised to prevent being understood as nakedness, and could rather be understood as a lack of torso protection : possibly naked, but probably in the sense of "lightly equipped" as with woolen or linen clothes as both represented in Gaulish sculpture (there with an upper protection, probably leathered or similar to linothorax armors) : Galatai/Galli would simply not have much torso protection. Even in late independent Gaul where mail armor was relatively more common for part of the troops, most of the armies (especially with a seemingly democratization of warfare by the IInd century) were likewise equipped of linen or woolen clothes wicker shields and some leather protections.
Polybus account itself is quite interesting : not only does it stresses that Gaisatai (Gaulish mercenaries) fought entierely naked, but also points that other Galatai fought with their usual light equipment, but that the formers discarded these not just as a display of confidence but also to fight more practically in a difficult ground. This would make a lot of sense tactically, as light infantry in ancient warfare tended to be both front of the lines and quite mobile in harassing the ennemy.
That we're talking of mercenaries there might be particularily relevant, as these were often made of bands of young men or poorer warriors anxious to proove themselves by gaining wealth, valour and social status in warfare : the display of confidence could be interpreted as a cultural or religious act bearing the likeness of heroics, youthful, divine-like warriors.
While restricting "fighting nakedness to young mercenaries would be pretty much speculative, it remains the main context we have for that on the mainland : possibly it was practiced elsewhere and by other warriors, but we lack evidence for that and it's hard not to consider that ancient authors, otherwise always searching for exotic and saucy details, did not mention them (such as Caesar in DBG) because it simply wasn't widely practiced enough.
It wasn't the end of the trope, however, and it found a new life in the description of northern peoples, as Germani (Tacitus, Germania, VI)^(5) , with their bodies painted over (Tacitus, Germania, XLIII)^(6) and bearing (sometimes barely) pants.
It is in this long-established representative context that the sources mentioned for ancient Britain by the article have to be understood and ,certainly, not acritically : both Caesar and Strabo stress that the lifestyle of southern Brittons were roughly the same than Gauls (we otherwise known being fashion-victims for coloufrul and quality clothes) and we have a broad description of Boudica's attire (Cassius Dio; History; LXII-2)^(7), elements that are corroborated by rare archeological evidence, such as the Bronze Age textiles found near Whitlesea (Cambridgeshire, England); or Amcotts Moor Woman' shoe (Lincolnshire) to which could be added the Baronstown West Man (County Kildare, Ireland) and his leather cloak; that would point that Brittons, indeed, probably didn't run around with their private parts for the world to see.
Note that these quotes do not concerns ancient Britain as a whole, however, but the indomitable Brittons that still holds out against the invaders northern Brittons that live besides the Roman province, peoples so remote from Roman rule, so poor and undevelloped that they're barely societies or even humans at all : certainly not worth the trouble invading them and turning them into something resembling Romans. It doesn't proove that these northernmost Brittons did not practiced heroic nakedness, especially in displaying body decorations (probably more body painting than tattoos, altough this is far from clear) and in context of raiding and warfare with Romans: unfortunately we don't have representation of indigenous peoples until the VIIth century (altough they seem pretty much not nude at this point).
Does that means "naked fighting" and "barbaric nakedness" were just Roman ethnographic clichés, carried over modern historical (mis)conceptions? While there are archeological and historical evidence for it, but set in a Roman representation of the Barbarian, uncivilized and far too remote from normalcy to ever be worth conquering or turning into real men; mixing elements from different social, military and even chronological contexts into a stereotype; with each author cannibalizing their predecessors' work (as it is quite obvious with Herodian) until a mangled cliché emerges from it, altough with the legitimacy classical litterary tradition got in modern eyes.
As such, it's not necessarily much more accurate than figuring Frenchmen as wearing striped shirts, a beret firmly put on their heads, smoking cigarettes in their Citroën 2CV, a baguette in the backseat waiting for the demonstration being over, to see a mime show. It's not that nothing of these do or did not exist, but the picture isn't real for that.
The success of such representations (as "Celtic" body painting) can be attributed to both their litterary fortune and the axiety of western cultures to set themselves in the cultural shadow of Romanity, with a popularized figuration of the Barbarian as barely clothed, foolishly brave, covered with "tribal" or "ethnic" tattoos of greater spiritual meaning, as the very recent representation of Ambiorix in Civilization VI new DLC is a perfect exemple of.
