Has the traditional pronunciation of Latin fallen completely out of favor in English, or do any prescriptivists still recommend it? Is it any more common in British English than in American?
A quick look through dictionaries reveals that Merriam-Webster is inconsistent, sometimes, but not always, omitting the traditional pronunciation altogether, whereas Oxford tends to list both.
I'm not asking about the position of classicists on this matter, but rather the position of Englishists.
It depends on what you mean, but for most interpretations of your question I think "fallen completely out of favor" would be an overstatement. I don't think there is a clear systematic difference between American English and British English; in fact, when I researched the pronunciation of the word algae, I found that British speakers seemed more likely than Americans to use "non-traditional" /g/, the opposite of the trend that you suggested.
I think almost nobody treats consistency as the highest priority for determining "correct" pronunciation, so whether a word is pronounced according to the "traditional" English pronunciation, "restored" pronunciation, a mix of both, or neither depends a lot on the identity of the word itself.
For example, the prescriptivist Charles Harrington Elster, author of the "Big Book of Beastly Mispronunciations", recommends using the pronunciation "DAY-tuh" for data "because it comes from Latin and follows the rules for the so-called English pronunciation of Latin" (p. 125), but he also gives the pronunciation of rationale as "RASH-uh-NAL" (p. 409) and quotes Bryan Garner, another author of usage advice, as saying that the pronunciation of rationale with non-silent final e "would sound terribly pedantic in most company".
I understand this question to be about, for example, whether one would be expected to pronounce Julius Caesar as djulius seezer, or alternatively as yoolius kaisar. The OP refers to traditional pronunciation, of which I take the former to be an example, but there are other factors that need to be considered: certain Latin words have become technical terms and have a particular pronunciation amongst those who use them as such (sine die is not pronounced 'seenay deeay', for example); some Latin words have entered common English and are pronounced without regard to traditional Latin pronunciation, and, probably most important, very few people these days have ever studied Latin and when confronted with Latin words pronounce them how they jolly well like.
An example of the last is the unpleasant bacterium clostridium difficile which in UK health circles is always pronounced as if the second word were French (which it looks as if it might be, but is not) and never as it would be if pronounced as classical Latin.
