There is always a question about linguistic conquest of a place: it is difficult to define how much language change indicates the arrival of new people rather than a switch for various other reasons including trade or other factors. What is clear is that there were two forms of Celtic language spoken in Britain and Ireland: Brittonic/Brythonic dominated Britain, and Goidelic was spoken in Ireland. At some point, Giodelic became the language of the Isle of Man and the western part of Caledonia and its islands (what is now known as Scotland), either through conquest, intermarriage, and/or trade.

With the arrival of the Romans in the first century, CE, Latin was introduced and was particularly influential in the south and east of Britain, but the Brittonic language apparently survived, little changed. With the withdrawal of Roman forces, Angles, Saxons, and Jutes began to colonize Britain, again being particularly dominant in the south and east of Britain. Their language, which we generally refer to at this period as Anglo-Saxon became progressively dominant as it spread with Anglo-Saxon power from the south and the east.

Brittonic languages fell out of fashion in one place after the next until holdouts existed in Wales and Cornwall. Anglo-Saxon and its subsequent forms, Middle English and Modern English, continued the process of linguistic conquest until it dominated much of Scotland and Cornwall and large parts of Wales and Ireland. Cornish was declared extinct by the beginning of the nineteenth century, although there are many references to survivors and survivals, and it now enjoys as revival. The same is true of Manx. In Cornwall - as is the case in Scotland and Ireland, some say that they can detect hints of the original Celtic language in the the local English dialect.

It is not easy to understand why language survived in some places more than others. The remote nature of what is known as the "Celtic fringe" - the far west of Cornwall, Wales, Scotland (and its islands), Brittany in north west France, and the far West of Ireland were all removed enough from centers of English power (or French power in the case of Brittany) that they escaped linguistic notice for longer than elsewhere. Aside from that, I'm not sure what you're asking, but that single observation may be what you seek.