We know from Roman writers the names (or Latinized versions of them) of many ancient British tribes that they encountered, the Iceni, Parisi, Trinovantes etc. but the Romans were rarely interested in recording or classifying the dialects that such barbarian tribes spoke. Romans were more interested in when the barbarians were going to become civilised and learn Latin.
It is often assumed that the Ancient Britons and Irish of the same period all spoke Celtic languages. We do have place or river names across much of Britain that appear to be Celtic survivals even in areas where the Celtic language died out a very long time ago e.g. in Eastern England there is a River Ouse in Bedford and another River Ouse in York, both of which seem to come from a Celtic word for 'water'. There are the surviving Welsh, Gaelic and Irish (and revived Cornish) Celtic languages in the West, and the limited record we have of the extinct Pictish language of North-East Scotland is usually taken to show that it was a Brythonic (related to Welsh) Celtic language.
However, the Celtic languages are a branch of the Indo-European language family that itself most likely began North of the Black Sea around 4,000 - 3,000 BC, the Celtic branch of which probably originated in Central Europe some time later, and eventually spread to Britain and Ireland, perhaps bringing the Bronze Age with them, apparently replacing whatever languages had been spoken in Britain previously.
How confident can we be that only Celtic languages were spoken in the British Isles when the Romans began their conquest of Britain in 43AD?
What is the likelihood that some pre-Celtic or other Continental related language was the native tongue of any tribe or community?