Did the passage from Latin to English, in England, help science flourish?

Maybe - but the link is tenuous, at best, I'd say - and may not even be causal.

The other answers correctly point out that, historically, science was the province of educated men, and these men would have learnt Latin and thus been able to read and communicate ideas (think Isaac Newton).

However, many of the technological advances of the English Industrial Revolution were not necessarily made by classically educated men - for example, Arkwright (water and steam powered mills), Stephenson (steam powered trains), Hargeaves (the spinning jenny). It is more likely that this profusion of non-classical engineers that spurred the transition away from Latin in science in general.

I'm not able to find definite evidence on, but I'm pretty sure that it was physics, mathematics and chemistry that transitioned away from Latin before biology and philosophy - showing how engineering brought English language into English science.

Something too long for a comment, and perhaps deserving of more than the potentially-ephemeral state of "comments":

First, specifically, in the late 1960s and through the 1970s, at least, for mathematics, a hugely significant fraction of important papers and textbooks were not in English. They were in French or German, and many things were in Russian, but the American Math Society translated some of them, with a year-or-two time lag.

When I was in grad school, it was absolutely essential to be able to read mathematical German and French (and Russian would have been good, but this was never available in high schools, and rarely in colleges/universities, but/and was luckily supplemented by AMS's translations).

That is, in those decades, there was no "Latin" for mathematics, at least.

But that was not a serious issue!

But, yes, then and now, less-devoted scholars, and "outsiders", will not have earlier anticipated the "need" to learn suitable languages... so, yes, certainly, coercing publications into a single vernacular language will make things more accessible.

That is, to recap, although multi-lingual science was never a serious obstacle for substantive professionals, it obviously could have been, and be so still, for people needing information that does not require comprehension of languages beyond their native one.

This is kind of a matter of opinion, but for what its worth, I don't think the change was particularly significant. First of all, it happened very gradually and during the time when most books were written in Latin, most anyone with even a basic education could read Latin. So, it was just not that big of a deal.

I think part of the problem is that the modern person thinks of "science" as this abstruse and formal course of studies and institutions based in universities. This is not the way science was practiced in the old days.

This question has no definite answer because there was no alternative. In the period between 17th and 19th century all science everywhere in Europe switched from the Latin to the native languages. This process was inevitable with the raise of nation-states. The argument that you cite is not valid, because before that time all educated people learned Latin. In fact ability to speak, write and read in Latin was the foundation of any education. This changed for the reasons which are independent of development of science, so science had to follow this general trend.

This trend had both positive and negative sides. Positive was that less education was required to learn science written in your native language. This made science accessible to more people. This is important, because many craftsmen who had no formal education obtained some access to scientific results. Negative was that communication between scientists of various countries became more difficult. This negative effect can be also demonstrated. Science in many countries (including England) became more isolated, and sometimes it took long time for important scientific results to spread across the boundaries.

Nowadays we have again the universal language of science (English) and we are essentially returning to the situation of 17th century when all science was written in one language. (The universality of English varies between various scientific disciplines). It is typical for a Russian and French scientist to correspond in English, like in 17th century, an English and a German scientist corresponded in Latin.

It is probably untrue that at the present time, the dominance of English has a negative effect on the development of science. (But again, we have no alternative history for comparison). Therefore one may conclude by comparison that switching from Latin to many languages had mixed overall effect.

EDIT. Of course one can say that English speakers have an advantage because their native language became international. The situation in the Middle Age was more fair:-) On the other hand, learning a foreign language seems to be beneficial to any child. Freeman Dyson once wrote that certain decline in English mathematics in 20th century can be attributed to the fact that students are not required anymore to learn Latin at school:-)