So is there any evidence that there were Britons fighting in the military of ancient Carthage?

No, there isn't.

While we don't have an exhaustive list of the peoples and regions Carthaginians recruited mercenaries from, Britons are never mentioned along Libyans, Numidians, Iberians, Celts (in the sense of southern Gauls), Italians, etc. troops.

there was some degree of Carthaginian trade with Britain

Indeed, Carthage, in this context Carthaginian as well as Ibero-Punic trade, had a privileged access to Atlantic trade, both trough the "Gallic Isthmus" (i.e. the Aude/Garonne rivers) and especially trough a firmly enforced ( u/PytheasTheMassaliot) dominance of coastal Atlantic navigation. This is observable, besides the account of Himilco's journey in the Atlantic up to Britain, one hundred years before Pytheas and recorded in the Ora Maritima, trough archaeological evidence along North African and Hispanic shores : trade goods (wine, pottery, beads, etc.), of course, coins, but also evidence of Punic or indigenous settlements (often but neither necessarily nor exclusively) trading places) closely related or influenced by Carthaginian culture. It seems quite probable that Carthaginian and Ibero-Punic polities had a similar commercial, cultural and societal influence on western and northern-western Hispanic peoples Greeks had on their own Gallic "Far-West".

Beyond that, however, Punic influence becomes much more scarcer.

There is, for instance, barely any evidence of a Carthaginian trade, let alone presence, in western and northern Gaul (in spite of the attraction of "phénicomanie" had in antiquarian and regionalist historiography) comparatively to evidenced commercial and cultural influence in its mediterranean parts, culminating with the Iberization of peoples between the Pyrénées and the Hérault river) and, of course, recruitment of local mercenaries.

There's, on the other hand, some room for debating a more important Punic influence in Britain : besides Himilco's and Pytheas' accounts, we have testimonies as Strabo's asserting that Kassiterides Islands^1 were formerly under Phoenician control and finding of coins that could be well understood within a context of tin trade with south-western Britain being probably its only main mining site in western Europe. But while sailing from Galicia to Cornwall would have been well within Punic traders means; the lack of harbours and stops along the way we could at least speculatively point out as part of Carthaginian trade from one hand, and the rarity of Punic goods besides, relatively, coinage from another hand, begs the question of how direct this trade might have been : Carthaginian adventurers and traders regularly meeting up to Cornwall and Scilly; or Gaulish traders carrying out tin against prestige goods up to Languedoc's harbours (that put Massalia in some shadow by the IVth century) as they did in pre-Roman times (Diodorus Siculus;V;22)?

And that have a direct importance when it comes to mercenariate : Libyans, Numidians, Iberians, Greeks, Gauls, etc. weren't randomly enlisted or just happened to pass trough the local "It's a Man's Life in Hamilcar's Army" recruiting booth but were peoples not only known but directly tied up to Mediterranean trade, Carthaginian soft or hard power, etc.

Along conscripted citizens, auxiliaries or even in some situation slaves (which wasn't more the norm to Carthaginians it was to Romans, still), mercenaries were recruited by xenologoi, as in Hellenistic armies, trusted with public budget raised on these ends but themselves private agents likely entrusted as they had good knowledge of the peoples they aimed to recruit, for their military and political reliance, but also their logistical capacity to join the army as it moved (Iberians, Gauls and Italians in Hannibal's army were thus recruited "along the way") or could be gathered and transported to (Elisyces, Ligurians and Celts from Southern Gaul to Sicily).

Where would Britons fit in there? A really peripheral people, whose contact with Carthaginians is arguably hard to assess but likely much more remote than those with Galicians, Celtiberians, Iberians, Celts, etc. which had a direct relation with Carthaginians and Puno-Iberians; and far from the regions of armed conflict in the Mediterranean basin without a lot of logistical structures to allow significant troops to move it quickly in.

Does that means there was never Britons mercenaries ever in Carthaginian armies? Obviously not : but between the absence of mention in classical sources and the broader situation, it sure seems a bit unlikely.

• Baray Luc; Celtes, Galates et Gaulois, mercenaires de l'Antiquité: représentation, recrutement, organisation.Paris: Éditions Picard, 2017

• Baray Luc; Les Celtes d'Hannibal; CNRS Editions; Paris; 2019

• González-Ruibal, Alfredo. Past the Last Outpost: Punic Merchants in the Atlantic Ocean (5th–1st century BC) in Journal of Mediterranean Archaeology 19 (1) pp 121–150; 2006

^1 It's worth mentioning, still, that Kassiterides as well as a lot of ultra-peripheral/half-mythified geographical names tend to "travel" around, and Kassiterides in this context might rather or together means islands on the Spanish coast