1) I fear we may be talking past each other here, so if you will allow me to clarify: I don't deny that Latin was spoken in Britannia. It would be stupid to consider otherwise, given that we know there were legions and outposts there for several centuries. But as to claims British Latin wasn't widely spoken, I will first admit that we don't have written evidence in great detail of spoken Brittonic either. But then there's the problem with determining the difference between Latin that happened to be spoken in Britain by Romans and immediate confederates, and anything resembling a Vulgar Latin descendant that could evolve into a Romance language. The few* sources I've noticed (the Vindolanda and Bath curse tablets) don't really betray any linguistic "localisms". That, combined with the near total replacement in the lowland zones by Old English (which shouldn't have happened if the Romans were still at least nominally in control, or so the logic seems to go), to me undermines the notion that Latin was anything more than a language of the Legion, and an interface between Roman politicians living there.
2) Would they? Not to be combative, but there seems to be (in your linked thesis as well) a fair amount of assumption without examples. I can buy bilingualism in Britannia on its face, but what evidence have we of a statistically significant Latin-only populace? And again, the dearth of British examples doesn't help establish a large Celtic-speaking population on its face, but then again didn't Gaul out-number Britannia in population by a fairly wide margin? Seems like a case of a much larger sample size than anything else (combined with a proximity issue with Britannia, compared to Gaul).
*And I do mean "few". For being a Roman province for several centuries, the fact that we only have a handful of tablets (only one of which apparently even addressing the Britons rather than being used by them, and in a derogatory way circa AD 100 no less) again does not convince me that Latin was widely spoken.
I think perhaps you should look at the evidence before making your assumptions, the paper I linked contained rather a lot of evidence based on detailed argument, reflecting the state of the art in historical linguistic studies. Your assumptions appear to be based on the idea that, if direct evidence is scarce, then you can choose to believe that Latin was marginal in Britain for most of the population. You actually need to provide evidence for your view, which you haven't as yet.
The evidence for Latin as a widespread spoken language is actually very strong. Just as strong as it is for Gaul in this period.
1. Textual evidence, curse tablets, graffiti, pottery inscriptions all attest popular use of written Latin. Funerary inscriptions attest to popular public ceremonial use of Latin.
2. Latin loanwords in Welsh and Cornish. These are incredibly frequent, there are about 700. These words include incredibly basic concepts like "dry", "fish", "arm", "green". Without widespread bilingualism, it is difficult to understand how this could have happened. It is best explained as an arrested process of language death, similar to that which was not arrested in Gaul.
3. The absence of Celtic loanwords in early Old English, but presence of Latin ones. The AS and Romano-Britons spoke Vulgar Latin as a common language in the early contact period, later switching to Anglo-Saxon.
4. The Bath curse tablets demonstrate phonetic features which are later attested in Welsh, suggesting that Latin speakers switched to Welsh influencing Welsh phonology (see Schrijver)
5. The Welsh word "Lloegr" ("England") came into existence prior to the arrival of Anglo-Saxons, clearly indicating a cultural distinction perceived by the Celtic highland zone. If England was largely Welsh speaking, why identify its inhabitants with an exonym?
6. Latin was the language of the British upper classes as late as the 5th century, the quality of Latin written by Gildas and Patrick is that of educated classical writers, they are not writing in the medieval latin of Bede and Nennius. The cultural and linguistic evidence from Roman villas and towns shows a thoroughly Latinised population, literate in Latin (documentary and funerary evidence included).
7. The population. Large numbers of merchants, civil servants, landowners, colonists, and soldiers were resident permanently in Britain. They lived in both urban and rural areas. All across the empire these people were the driving force in the adoption of vernacular Latin, why not in Britain?
For British Latin to exist, it is not necessary to prove substantial "non-standard" localisms, and widespread British Latin is all you need to create a situation where England speaks a Romance language. Of course, you need a POD that allows British Latin political control, which is practically difficult as we know so little about 5th century Britian.