Read the following extract. I’ve linked to the source as well.
"However, there is one thing that the Romans, modern archaeologists and the Iron Age islanders themselves would all agree on: they were not Celts. This was an invention of the 18th century; the name was not used earlier. The idea came from the discovery around 1700 that the non-English island tongues relate to that of the ancient continental Gauls, who really were called Celts. This ancient continental ethnic label was applied to the wider family of languages. But ‘Celtic’ was soon extended to describe insular monuments, art, culture and peoples, ancient and modern: island ‘Celtic’ identity was born, like Britishness, in the 18th century.
However, language does not determine ethnicity (that would make the modern islanders ‘Germans’, since they mostly speak English, classified as a Germanic tongue). And anyway, no one knows how or when the languages that we choose to call ‘Celtic’, arrived in the archipelago - they were already long established and had diversified into several tongues, when our evidence begins. Certainly, there is no reason to link the coming of ‘Celtic’ language with any great ‘Celtic invasions’ from Europe during the Iron Age, because there is no hard evidence to suggest there were any."
I incorrectly thought it was a Victorian invention; apparently it started in the reign of William & Mary.