Both these answers could contain elements that might interest you.

It's important to keep in mind that romanization doesn't really describe a precise phenomenon of native acculturation from "less" to "more" Roman, but several realities of provincial (or even extra-provincial, in the case of Germania) creolization. A Greek-speaking denizen of a Syrian town could be considered romanized in the same broad sense than a Gallic villa-owner speaking both Gaulish and Latin, that a Britton-speaking supplier of a Roman garrison in the Hadrian Wall, or that a Berberophone middle-class whose sons would marry with Roman families.

Integration into the roman horizon was first of all defined by the relation populations had with the Roman state, not just paying tributes, tolls and/or taxes; but also partaking into its laws, obeying them, having access to provincial functions etc. Romans didn't particularly searched to Latinize the provinces, but to make them integrated as much as it was possible to this political ensemble.

Gaul, its southern part than the whole of it, was early on integrated within the broad Roman "zone of influence" both politically and economically, to the point southern Gaul was already considered a "Little Italy" in the first century AD. Even before the Roman conquest, polities and factional interests were already largely tied to Rome : as a social class, they depended from maintained ties with it especially as the new rulers redrawn the political organization of the region in order to better control and pacify the region. Archeologically, there's a strong sense of continuity, even if Gauls began to adopt Roman practices for themselves, religiously or socially such as change in food by eating bread, "translating" or transforming their head-cities into Roman agglomerations, adopting Latin (which was already a language of prestige) as a sociolect, etc. The very liberal and early attribution of Latin then Roman Law to Gauls as a whole, meaning a legal preponderance of Latin in their immediate lives, certainly played an important role there as well comparatively to Britain but as well Africa (where Berber well survived even on the coast).

They didn't stop thinking themselves as Gauls, but began to do so on Roman lines : old ties being maintained, you didn't have a great cultural division between native elites and lower classes and while these probably kept speaking Gaulish well into Late Antiquity (although only remotely by the VIth century, and especially in peripheral regions) maintained contact between with latinized elites allowed a smoother and more entire linguistic transmission.

Britain is a more complex case : while the southern British petty-states entered a very strong relation with the Roman Empire as well (probably even more so than between Gaulish petty-states and the Late Republic), a good part of the island was politically less integrated and the longer conquest can attest from that either by the need of gradual advances or crushing revolts, with the province being fairly more militarized in respect to its population than Gaul or Spain.

Not that Romans leaved no marks in Britain, and pretending it would be absurdly wrong giving the sheer importance of archeological finds. But these cities, these products, these markers of Roman civilization are more easily present in the southern-eastern regions (the very same that were better integrated and kept being so to the Mediterranean world) than in the rest where archeological continuity from the pre-Roman period is dominant and/or where Romanity was first exprimed and made possible by military presence (which itself certainly had a linguistic impact). Only in the southern third of the provinces would you find a region fairly comparable to Gaul and even quite possibly Latinized (at least on an unequal bilingual relation with Britton). Latin was probably important as lingua franca, institutional and prestige language everywhere else; but possibly only "rooted down" in regions that suffered the most from the consequences of the decline of the western Roman state such as the gradual disappearance of villae and urban towns by the Vth century; while they were also the regions most settled by waves after waves of newcomers from the North Sea that, comparatively to "mainland Barbarians" as Franks or Goths, had much fewer interactions and exchanges with Romans as "peoples of the border" and thus less romanized themselves; ending up with the emergence of new political and cultural identities. Note that the others regions, less or poorly touched by a constant Roman influence ended up undergoing similar political emergence on indigenous lines that did not discarded romanity and Latin but mostly expressed it trough symbolical and monumental epigraphy and connection to Latin Christianity, but not as an usual language.

Celtic languages can be divided between Continental and Insular, and then the Insular Celtic languages can be divided between Goidelic and Brythonic. Confusingly enough Breton, while being on the continent, is an Insular Celtic language, being brought to Brittany from the islands and is therefor only a relative of the Gaulish language that would eventually influence the Romance language in Gaul and be replaced, not a descendant. The Latin language spoken in Gaul was a language of prestige because it was the language of commerce, the language of the conquerors, and it was also a written language.

The Celtic languages the romans would have encountered in Gaul were completely displaced. The Celtic languages in Britain however did not fair much better, after the Roman Empire fell there were Germanic and Norse invasions that further displaced the Brythonic Celtic languages, almost completely eradicating them from what is now England and pushing them to the corners of what is now Cornwall and Wales.

It’s also important to note that there were Brythonic languages spoken in modern day Scotland, Cumbric and Pictish, that were replaced by Goidelic Celtic languages, which would become today’s Gaelic.

Latin in Gaul was around long enough that it not only was a language one learned to do business with traveling merchants, but a language that would grant the speaker some sort of social mobility within the empire so over time, the type of Vulgar Latin spoken there was taught to children and became a community language. In Britain however Rome didn’t have the same level of influence and control, so when the empire fell their language mostly went home with the soldiers. (Without a Roman presence on the island, however, the Celts would fall much more dramatically under the Germanic speaking Anglos, Saxons, and Jutes.